Cluster analysis - Knowledge

1932:. In contrast to many newer methods, it features a well-defined cluster model called "density-reachability". Similar to linkage-based clustering, it is based on connecting points within certain distance thresholds. However, it only connects points that satisfy a density criterion, in the original variant defined as a minimum number of other objects within this radius. A cluster consists of all density-connected objects (which can form a cluster of an arbitrary shape, in contrast to many other methods) plus all objects that are within these objects' range. Another interesting property of DBSCAN is that its complexity is fairly low – it requires a linear number of range queries on the database – and that it will discover essentially the same results (it is 1641: 1653: 1788: 1828:, a canonical problem in the operations research and computational geometry communities. In a basic facility location problem (of which there are numerous variants that model more elaborate settings), the task is to find the best warehouse locations to optimally service a given set of consumers. One may view "warehouses" as cluster centroids and "consumer locations" as the data to be clustered. This makes it possible to apply the well-developed algorithmic solutions from the facility location literature to the presently considered centroid-based clustering problem. 2043: 2018:. Eventually, objects converge to local maxima of density. Similar to k-means clustering, these "density attractors" can serve as representatives for the data set, but mean-shift can detect arbitrary-shaped clusters similar to DBSCAN. Due to the expensive iterative procedure and density estimation, mean-shift is usually slower than DBSCAN or k-Means. Besides that, the applicability of the mean-shift algorithm to multidimensional data is hindered by the unsmooth behaviour of the kernel density estimate, which results in over-fragmentation of cluster tails. 11211: 2058: 1893: 1803: 1909: 2028: 11197: 8901: 8881: 5090: 11235: 11223: 2265:

internal criteria in cluster evaluation is that high scores on an internal measure do not necessarily result in effective information retrieval applications. Additionally, this evaluation is biased towards algorithms that use the same cluster model. For example, k-means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering.

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kind of structure exists in the data set. An algorithm designed for some kind of models has no chance if the data set contains a radically different set of models, or if the evaluation measures a radically different criterion. For example, k-means clustering can only find convex clusters, and many evaluation indexes assume convex clusters. On a data set with non-convex clusters neither the use of

1760:– to be specified in advance, which is considered to be one of the biggest drawbacks of these algorithms. Furthermore, the algorithms prefer clusters of approximately similar size, as they will always assign an object to the nearest centroid. This often leads to incorrectly cut borders of clusters (which is not surprising since the algorithm optimizes cluster centers, not cluster borders). 1462:, is based on the core idea of objects being more related to nearby objects than to objects farther away. These algorithms connect "objects" to form "clusters" based on their distance. A cluster can be described largely by the maximum distance needed to connect parts of the cluster. At different distances, different clusters will form, which can be represented using a 1470:" comes from: these algorithms do not provide a single partitioning of the data set, but instead provide an extensive hierarchy of clusters that merge with each other at certain distances. In a dendrogram, the y-axis marks the distance at which the clusters merge, while the objects are placed along the x-axis such that the clusters don't mix. 2950:: Purity is a measure of the extent to which clusters contain a single class. Its calculation can be thought of as follows: For each cluster, count the number of data points from the most common class in said cluster. Now take the sum over all clusters and divide by the total number of data points. Formally, given some set of clusters 1493:("Unweighted or Weighted Pair Group Method with Arithmetic Mean", also known as average linkage clustering). Furthermore, hierarchical clustering can be agglomerative (starting with single elements and aggregating them into clusters) or divisive (starting with the complete data set and dividing it into partitions). 5388:. It also may be used to return a more comprehensive set of results in cases where a search term could refer to vastly different things. Each distinct use of the term corresponds to a unique cluster of results, allowing a ranking algorithm to return comprehensive results by picking the top result from each cluster. 1442:

another. An algorithm that is designed for one kind of model will generally fail on a data set that contains a radically different kind of model. For example, k-means cannot find non-convex clusters. Most traditional clustering methods assume the clusters exhibit a spherical, elliptical or convex shape.

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The Fowlkes–Mallows index computes the similarity between the clusters returned by the clustering algorithm and the benchmark classifications. The higher the value of the Fowlkes–Mallows index the more similar the clusters and the benchmark classifications are. It can be computed using the following

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for evaluation. These types of evaluation methods measure how close the clustering is to the predetermined benchmark classes. However, it has recently been discussed whether this is adequate for real data, or only on synthetic data sets with a factual ground truth, since classes can contain internal

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Therefore, the internal evaluation measures are best suited to get some insight into situations where one algorithm performs better than another, but this shall not imply that one algorithm produces more valid results than another. Validity as measured by such an index depends on the claim that this

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The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms. There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different

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In external evaluation, clustering results are evaluated based on data that was not used for clustering, such as known class labels and external benchmarks. Such benchmarks consist of a set of pre-classified items, and these sets are often created by (expert) humans. Thus, the benchmark sets can be

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When a clustering result is evaluated based on the data that was clustered itself, this is called internal evaluation. These methods usually assign the best score to the algorithm that produces clusters with high similarity within a cluster and low similarity between clusters. One drawback of using

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External evaluation has similar problems: if we have such "ground truth" labels, then we would not need to cluster; and in practical applications we usually do not have such labels. On the other hand, the labels only reflect one possible partitioning of the data set, which does not imply that there

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These methods will not produce a unique partitioning of the data set, but a hierarchy from which the user still needs to choose appropriate clusters. They are not very robust towards outliers, which will either show up as additional clusters or even cause other clusters to merge (known as "chaining

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There is no objectively "correct" clustering algorithm, but as it was noted, "clustering is in the eye of the beholder." The most appropriate clustering algorithm for a particular problem often needs to be chosen experimentally, unless there is a mathematical reason to prefer one cluster model over

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More than a dozen of internal evaluation measures exist, usually based on the intuition that items in the same cluster should be more similar than items in different clusters. For example, the following methods can be used to assess the quality of clustering algorithms based on internal criterion:

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Neither of these approaches can therefore ultimately judge the actual quality of a clustering, but this needs human evaluation, which is highly subjective. Nevertheless, such statistics can be quite informative in identifying bad clusterings, but one should not dismiss subjective human evaluation.

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Internal evaluation measures suffer from the problem that they represent functions that themselves can be seen as a clustering objective. For example, one could cluster the data set by the Silhouette coefficient; except that there is no known efficient algorithm for this. By using such an internal

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As listed above, clustering algorithms can be categorized based on their cluster model. The following overview will only list the most prominent examples of clustering algorithms, as there are possibly over 100 published clustering algorithms. Not all provide models for their clusters and can thus

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is that they expect some kind of density drop to detect cluster borders. On data sets with, for example, overlapping Gaussian distributions – a common use case in artificial data – the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases

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This measure doesn't penalize having many clusters, and more clusters will make it easier to produce a high purity. A purity score of 1 is always possible by putting each data point in its own cluster. Also, purity doesn't work well for imbalanced data, where even poorly performing clustering

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data set. In this technique, we create a grid structure, and the comparison is performed on grids (also known as cells). The grid-based technique is fast and has low computational complexity. There are two types of grid-based clustering methods: STING and CLIQUE. Steps involved in grid-based

2676:. Since algorithms that produce clusters with low intra-cluster distances (high intra-cluster similarity) and high inter-cluster distances (low inter-cluster similarity) will have a low Davies–Bouldin index, the clustering algorithm that produces a collection of clusters with the smallest 2188:

family of algorithms) have been adapted to subspace clustering (HiSC, hierarchical subspace clustering and DiSH) and correlation clustering (HiCO, hierarchical correlation clustering, 4C using "correlation connectivity" and ERiC exploring hierarchical density-based correlation clusters).

1844:. This approach models the data as arising from a mixture of probability distributions. It has the advantages of providing principled statistical answers to questions such as how many clusters there are, what clustering method or model to use, and how to detect and deal with outliers. 4615:

To measure cluster tendency is to measure to what degree clusters exist in the data to be clustered, and may be performed as an initial test, before attempting clustering. One way to do this is to compare the data against random data. On average, random data should not have clusters.

4577:. This index scores positively the fact that the labels are as sparse as possible across the clusters, i.e., that each cluster has as few different labels as possible. The higher the value of the Chi Index the greater the relationship between the resulting clusters and the label used. 1318:

A "clustering" is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. Clusterings can be roughly distinguished as:

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The silhouette coefficient contrasts the average distance to elements in the same cluster with the average distance to elements in other clusters. Objects with a high silhouette value are considered well clustered, objects with a low value may be outliers. This index works well with

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Cluster analysis can be used to identify areas where there are greater incidences of particular types of crime. By identifying these distinct areas or "hot spots" where a similar crime has happened over a period of time, it is possible to manage law enforcement resources more

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algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:

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The Dunn index aims to identify dense and well-separated clusters. It is defined as the ratio between the minimal inter-cluster distance to maximal intra-cluster distance. For each cluster partition, the Dunn index can be calculated by the following formula:

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such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster. Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques, as in the

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between attributes. However, these algorithms put an extra burden on the user: for many real data sets, there may be no concisely defined mathematical model (e.g. assuming Gaussian distributions is a rather strong assumption on the data).

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In density-based clustering, clusters are defined as areas of higher density than the remainder of the data set. Objects in sparse areas – that are required to separate clusters – are usually considered to be noise and border points.

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algorithms will give a high purity value. For example, if a size 1000 dataset consists of two classes, one containing 999 points and the other containing 1 point, then every possible partition will have a purity of at least 99.9%.

3764: 1875:, so multiple runs may produce different results. In order to obtain a hard clustering, objects are often then assigned to the Gaussian distribution they most likely belong to; for soft clusterings, this is not necessary. 4049: 5414:

Clustering is useful in software evolution as it helps to reduce legacy properties in code by reforming functionality that has become dispersed. It is a form of restructuring and hence is a way of direct preventative

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takes on a value between 0 and 1. An index of 1 means that the two dataset are identical, and an index of 0 indicates that the datasets have no common elements. The Jaccard index is defined by the following formula:

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Clustering can be used to group all the shopping items available on the web into a set of unique products. For example, all the items on eBay can be grouped into unique products (eBay does not have the concept of a

3094: 1111:. The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest. 5454:

Recommender systems are designed to recommend new items based on a user's tastes. They sometimes use clustering algorithms to predict a user's preferences based on the preferences of other users in the user's

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Clustering may be used to identify different niches within the population of an evolutionary algorithm so that reproductive opportunity can be distributed more evenly amongst the evolving species or subspecies.

1032:. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small 5290:

Cluster analysis can be used to analyse patterns of antibiotic resistance, to classify antimicrobial compounds according to their mechanism of action, to classify antibiotics according to their antibacterial

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unless constraints are put on the model complexity. A more complex model will usually be able to explain the data better, which makes choosing the appropriate model complexity inherently difficult. Standard

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If the density of a neighboring cell is greater than threshold density then, add the cell in the cluster and repeat steps 4.2 and 4.3 till there is no neighbor with a density greater than threshold density.

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Gao, Caroline X.; Dwyer, Dominic; Zhu, Ye; Smith, Catherine L.; Du, Lan; Filia, Kate M.; Bayer, Johanna; Menssink, Jana M.; Wang, Teresa; Bergmeir, Christoph; Wood, Stephen; Cotton, Sue M. (2023-09-01).

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From poll data, projects such as those undertaken by the Pew Research Center use cluster analysis to discern typologies of opinions, habits, and demographics that may be useful in politics and marketing.

2142:, which can process huge data sets efficiently, but the resulting "clusters" are merely a rough pre-partitioning of the data set to then analyze the partitions with existing slower methods such as 1646:

Single-linkage on Gaussian data. At 35 clusters, the biggest cluster starts fragmenting into smaller parts, while before it was still connected to the second largest due to the single-link effect.

1477:, the user also needs to decide on the linkage criterion (since a cluster consists of multiple objects, there are multiple candidates to compute the distance) to use. Popular choices are known as 2299: 2932:

A number of measures are adapted from variants used to evaluate classification tasks. In place of counting the number of times a class was correctly assigned to a single data point (known as

6181:; Sander, Jörg; Xu, Xiaowei (1996). "A density-based algorithm for discovering clusters in large spatial databases with noise". In Simoudis, Evangelos; Han, Jiawei; Fayyad, Usama M. (eds.). 3197: 4214: 3430: 2883:. Since internal criterion seek clusters with high intra-cluster similarity and low inter-cluster similarity, algorithms that produce clusters with high Dunn index are more desirable. 4911: 1585: 7628:

Remm, Maido; Storm, Christian E. V.; Sonnhammer, Erik L. L. (2001-12-14). "Automatic clustering of orthologs and in-paralogs from pairwise species comparisons11Edited by F. Cohen".

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A confusion matrix can be used to quickly visualize the results of a classification (or clustering) algorithm. It shows how different a cluster is from the gold standard cluster.

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In the process of intelligent grouping of the files and websites, clustering may be used to create a more relevant set of search results compared to normal search engines like

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Bewley, A., & Upcroft, B. (2013). Advantages of Exploiting Projection Structure for Segmenting Dense 3D Point Clouds. In Australian Conference on Robotics and Automation

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Cluster analysis is used to describe and to make spatial and temporal comparisons of communities (assemblages) of organisms in heterogeneous environments. It is also used in

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The Rand index computes how similar the clusters (returned by the clustering algorithm) are to the benchmark classifications. It can be computed using the following formula:

2620: 2042: 5768: 3497: 1986: 1958: 2700: 2524: 2138:), the willingness to trade semantic meaning of the generated clusters for performance has been increasing. This led to the development of pre-clustering methods such as 1674:

In centroid-based clustering, each cluster is represented by a central vector, which is not necessarily a member of the data set. When the number of clusters is fixed to

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R. Ng and J. Han. "Efficient and effective clustering method for spatial data mining". In: Proceedings of the 20th VLDB Conference, pages 144–155, Santiago, Chile, 1994.

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Achtert, E.; Böhm, C.; Kröger, P. (2006). "DeLi-Clu: Boosting Robustness, Completeness, Usability, and Efficiency of Hierarchical Clustering by a Closest Pair Ranking".

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metric; another provides hierarchical clustering. Using genetic algorithms, a wide range of different fit-functions can be optimized, including mutual information. Also

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are equally weighted. This may be an undesirable characteristic for some clustering applications. The F-measure addresses this concern, as does the chance-corrected

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is the number of pairs of points that are clustered together in the predicted partition but not in the ground truth partition etc. If the dataset is of size N, then

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and these models can usually be characterized as similar to one or more of the above models, and including subspace models when neural networks implement a form of

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Single-linkage on density-based clusters. 20 clusters extracted, most of which contain single elements, since linkage clustering does not have a notion of "noise".

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measure of how much information is shared between a clustering and a ground-truth classification that can detect a non-linear similarity between two clusterings.

5397:'s map of photos and other map sites use clustering to reduce the number of markers on a map. This makes it both faster and reduces the amount of visual clutter. 4431: 4404: 4377: 4350: 4139: 4116: 4079: 3903: 3355: 3332: 3301: 3274: 3247: 3224: 4784: 4764: 4691: 4671: 4651: 4478: 4458: 3664: 3640: 3008: 2988: 2968: 2544: 2497: 2929:, where meta information (such as class labels) is used already in the clustering process, the hold-out of information for evaluation purposes is non-trivial. 2057: 3675: 880: 7671:

Botstein, David; Cox, David R.; Risch, Neil; Olshen, Richard; Curb, David; Dzau, Victor J.; Chen, Yii-Der I.; Hebert, Joan; Pesich, Robert (2001-07-01).

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Kraskov, Alexander; Stögbauer, Harald; Andrzejak, Ralph G.; Grassberger, Peter (1 December 2003). "Hierarchical Clustering Based on Mutual Information".

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Pfitzner, Darius; Leibbrandt, Richard; Powers, David (2009). "Characterization and evaluation of similarity measures for pairs of clusterings".

10332: 7112: 4237: 918: 1716:-means often include such optimizations as choosing the best of multiple runs, but also restricting the centroids to members of the data set ( 10837: 5064:

With this definition, uniform random data should tend to have values near to 0.5, and clustered data should tend to have values nearer to 1.

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Clustering can be used to divide a fluence map into distinct regions for conversion into deliverable fields in MLC-based Radiation Therapy.

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measure for evaluation, one rather compares the similarity of the optimization problems, and not necessarily how useful the clustering is.

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Cluster analysis is used to identify patterns of family life trajectories, professional careers, and daily or weekly time use for example.

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Connectivity-based clustering is a whole family of methods that differ by the way distances are computed. Apart from the usual choice of

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Cluster analysis is used to reconstruct missing bottom hole core data or missing log curves in order to evaluate reservoir properties.

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cluster centers and assign the objects to the nearest cluster center, such that the squared distances from the cluster are minimized.

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Di Marco, Antonio; Navigli, Roberto (2013). "Clustering and Diversifying Web Search Results with Graph-Based Word Sense Induction".

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continuously. On a data set consisting of mixtures of Gaussians, these algorithms are nearly always outperformed by methods such as

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that are initialized randomly and whose parameters are iteratively optimized to better fit the data set. This will converge to a

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This is simply the number of unique elements common to both sets divided by the total number of unique elements in both sets.

2433:{\displaystyle DB={\frac {1}{n}}\sum _{i=1}^{n}\max _{j\neq i}\left({\frac {\sigma _{i}+\sigma _{j}}{d(c_{i},c_{j})}}\right)} 1223:(also known as co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes. 986:(in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task of 5837:

Cluster Analysis: Correlation Profile and Orthometric (factor) Analysis for the Isolation of Unities in Mind and Personality

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K-means has a number of interesting theoretical properties. First, it partitions the data space into a structure known as a

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Hopkins, Brian; Skellam, John Gordon (1954). "A new method for determining the type of distribution of plant individuals".

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is the number of pairs of points that are clustered together in the predicted partition and in the ground truth partition,

1428: 895: 658: 193: 5775:. Quantitative Expression of Cultural Relationships. Berkeley, CA: University of California Press: 211–256. Archived from 2940:

metrics assess whether each pair of data points that is truly in the same cluster is predicted to be in the same cluster.

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point of view, the reproduction of known knowledge may not necessarily be the intended result. In the special scenario of

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Anomalies/outliers are typically – be it explicitly or implicitly – defined with respect to clustering structure in data.

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Evaluation (or "validation") of clustering results is as difficult as the clustering itself. Popular approaches involve "

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However, data containing just a single Gaussian will also score close to 1, as this statistic measures deviation from a

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In recent years, considerable effort has been put into improving the performance of existing algorithms. Among them are

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for core and noise points, but not for border points) in each run, therefore there is no need to run it multiple times.

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Agrawal, R.; Gehrke, J.; Gunopulos, D.; Raghavan, P. (2005). "Automatic Subspace Clustering of High Dimensional Data".

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Clustering algorithms are used for robotic situational awareness to track objects and detect outliers in sensor data.

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Peter J. Rousseeuw (1987). "Silhouettes: A graphical aid to the interpretation and validation of cluster analysis".

11239: 10812: 10686: 8674: 5615: 4558: 2158: 2027: 1182: 452: 90: 4146: 4087: 2879:) may be measured in a variety of ways, such as the maximal distance between any pair of elements in cluster 1591:, which makes them too slow for large data sets. For some special cases, optimal efficient methods (of complexity 1350:): each object belongs to each cluster to a certain degree (for example, a likelihood of belonging to the cluster) 10870: 10531: 10276: 9647: 9237: 5605: 3360: 1284:

has exactly one negative edge) yields results with more than two clusters, or subgraphs with only positive edges.

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into market segments and to better understand the relationships between different groups of consumers/potential

5053:{\displaystyle H={\frac {\sum _{i=1}^{m}{u_{i}^{d}}}{\sum _{i=1}^{m}{u_{i}^{d}}+\sum _{i=1}^{m}{w_{i}^{d}}}}\,,} 1052:

and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of

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or clusters of organisms (individuals) at the species, genus or higher level that share a number of attributes.

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Luna-Romera, José María; Martínez-Ballesteros, María; García-Gutiérrez, Jorge; Riquelme, José C. (June 2019).

2165:(where only some attributes are used, and cluster models include the relevant attributes for the cluster) and 1771:. Third, it can be seen as a variation of model-based clustering, and Lloyd's algorithm as a variation of the 11164: 10123: 9026: 8394: 8083: 1544: 1234:: some algorithms do not provide a refined model for their results and just provide the grouping information. 1056:

or interactive multi-objective optimization that involves trial and failure. It is often necessary to modify

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To find structural similarity, etc., for example, 3000 chemical compounds were clustered in the space of 90

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is a generalization of DBSCAN that removes the need to choose an appropriate value for the range parameter

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Cluster analysis originated in anthropology by Driver and Kroeber in 1932 and introduced to psychology by

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is a family of corrected-for-chance variants of this that has a reduced bias for varying cluster numbers.

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Cluster analysis is for example used to identify groups of schools or students with similar properties.

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that also looks for arbitrary rotated ("correlated") subspace clusters that can be modeled by giving a

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problem. The appropriate clustering algorithm and parameter settings (including parameters such as the

890: 817: 567: 462: 250: 183: 143: 7913: 2157:, which renders particular distance functions problematic in high-dimensional spaces. This led to new 11261: 10676: 10444: 10165: 10090: 10019: 9948: 9868: 9856: 9726: 9714: 9707: 9415: 9136: 8912: 8770: 8409: 8240: 8063: 5722: 5667: 4223: 2015: 1965: 1825: 1498: 1478: 987: 944: 550: 318: 188: 7844: 6901: 6846: 6622: 6524: 6454: 6228: 2812:{\displaystyle D={\frac {\min _{1\leq i<j\leq n}d(i,j)}{\max _{1\leq k\leq n}d^{\prime }(k)}}\,,} 2576: 11159: 10926: 10789: 10474: 10439: 10403: 10188: 9630: 9539: 9498: 9410: 9101: 8940: 8811: 8068: 7192: 7056: 7054: 7052: 6736: 6575: 6256: 5710: 5645: 5458: 5254: 5187: 2677: 2291: 2282: 2198: 2077: 1857: 1841: 1255: 1037: 572: 492: 415: 333: 163: 125: 120: 80: 75: 6677: 6183:

Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96)

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Estivill-Castro, Vladimir (20 June 2002). "Why so many clustering algorithms – A Position Paper".

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structure, the attributes present may not allow separation of clusters or the classes may contain

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is a clustering approach where each object is moved to the densest area in its vicinity, based on

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of the covariance matrices, that provide a balance between overfitting and fidelity to the data.

1796:-means separates data into Voronoi cells, which assumes equal-sized clusters (not adequate here). 1767:. Second, it is conceptually close to nearest neighbor classification, and as such is popular in 1467: 1458: 1451: 1152: 519: 368: 268: 95: 7049: 5075:, making this statistic largely useless in application (as real data never is remotely uniform). 4876: 4816: 2867:) between two clusters may be any number of distance measures, such as the distance between the 1434:

not easily be categorized. An overview of algorithms explained in Knowledge can be found in the

1280:, edges may change sign and result in a bifurcated graph. The weaker "clusterability axiom" (no 978:

is the task of grouping a set of objects in such a way that objects in the same group (called a

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Hartuv, Erez; Shamir, Ron (2000-12-31). "A clustering algorithm based on graph connectivity".

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Fowlkes, E. B.; Mallows, C. L. (1983). "A Method for Comparing Two Hierarchical Clusterings".

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Proceedings of the 2004 ACM SIGMOD international conference on Management of data - SIGMOD '04

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Cattell, R. B. (1943). "The description of personality: Basic traits resolved into clusters".

3836: 3773: 2230:" evaluation, where the clustering is compared to an existing "ground truth" classification, " 11131: 11073: 11016: 10842: 10735: 10644: 10370: 10254: 10113: 10105: 9995: 9987: 9802: 9698: 9676: 9635: 9600: 9567: 9513: 9488: 9443: 9382: 9342: 9144: 8967: 8846: 8831: 8796: 8484: 8384: 8252: 7831: 7098: 6833: 5942:"An overview of clustering methods with guidelines for application in mental health research" 5620: 5226: 3799: 2150: 1868: 1296: 1246: 1006: 653: 475: 427: 283: 198: 70: 8714: 6728:

19th International Conference on Scientific and Statistical Database Management (SSDBM 2007)

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Cluster analysis is widely used in market research when working with multivariate data from

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Clustering is often utilized to locate and characterize extrema in the target distribution.

5234: 4849: 4789: 4722: 4495: 2913: 2652: 2625: 2549: 2451: 1728: 1697: 1281: 1045: 582: 532: 6614:

18th International Conference on Scientific and Statistical Database Management (SSDBM'06)

6385: 1712:, and is commonly run multiple times with different random initializations. Variations of 8: 11201: 11126: 11049: 10730: 10494: 10487: 10449: 10357: 10337: 10309: 10042: 9908: 9903: 9893: 9885: 9703: 9664: 9554: 9544: 9453: 9232: 9188: 9106: 9031: 8933: 8441: 8419: 8168: 8163: 8121: 8073: 5747: 5700: 5655: 5650: 5610: 5449: 5329: 5222: 3920: 3911: 3449: 2922: 2211: 2162: 1588: 1412: 1303: 1265: 1107: 1053: 1048:

to use, a density threshold or the number of expected clusters) depend on the individual

998: 685: 621: 592: 497: 323: 256: 242: 228: 203: 153: 105: 65: 34:

The result of a cluster analysis shown as the coloring of the squares into three clusters

7932: 7230:

Proceedings of the 17th International Conference on Extending Database Technology (EDBT)

6892: 6825: 4413: 4386: 4359: 4332: 4121: 4098: 4061: 3885: 3337: 3314: 3283: 3256: 3229: 3206: 11215: 11026: 10880: 10776: 10725: 10601: 10498: 10482: 10459: 10236: 9970: 9953: 9913: 9824: 9719: 9681: 9652: 9612: 9572: 9518: 9435: 9121: 9116: 8826: 8404: 7952: 7914:"Classifications of Atmospheric Circulation Patterns: Recent Advances and Applications" 7797: 7754: 7729: 7575: 7524: 7487: 7456: 7424: 7365: 7315: 7280: 7262: 7184: 6964: 6922: 6811: 6759: 6719: 6700: 6645: 6558: 6507: 6485: 6467: 6422: 6398: 6358: 6214:; Sander, Jörg (1999). "OPTICS: Ordering Points To Identify the Clustering Structure". 6211: 6178: 6140: 6112: 6094: 5905: 5683: 5435: 5418: 5409: 5348: 5313: 4769: 4749: 4676: 4656: 4636: 4587: 4582: 4463: 4443: 3649: 3625: 2993: 2973: 2953: 2529: 2482: 2203: 2193: 2143: 1867:). Here, the data set is usually modeled with a fixed (to avoid overfitting) number of 1679: 1669: 1273: 1076: 1057: 983: 663: 587: 373: 168: 7705: 7606: 7414:. European Chapter of the Association for Computational Linguistics. pp. 345–355. 3759:{\displaystyle F_{\beta }={\frac {(\beta ^{2}+1)\cdot P\cdot R}{\beta ^{2}\cdot P+R}}} 2943:

As with internal evaluation, several external evaluation measures exist, for example:

2238:" evaluation by evaluating the utility of the clustering in its intended application. 2051:

assumes clusters of similar density, and may have problems separating nearby clusters.

11210: 11121: 11091: 11083: 10903: 10894: 10819: 10750: 10606: 10591: 10566: 10454: 10395: 10261: 10249: 9875: 9792: 9736: 9659: 9503: 9425: 9204: 9078: 8892: 8880: 8684: 8336: 8207: 8200: 7987: 7944: 7897: 7880: 7759: 7745: 7710: 7692: 7653: 7645: 7610: 7567: 7559: 7514: 7369: 7166: 7106: 7066: 7038: 7028: 7002: 6992: 6914: 6879:

Frey, B. J.; Dueck, D. (2007). "Clustering by Passing Messages Between Data Points".

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Cluster analysis refers to a family of algorithms and tasks rather than one specific

1018: 756: 599: 512: 308: 278: 223: 218: 173: 115: 7956: 7528: 7460: 6362: 6144: 6098: 5259:

The similarity of genetic data is used in clustering to infer population structures.

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is an external validation index that measure the clustering results by applying the

1878:

Distribution-based clustering produces complex models for clusters that can capture

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Rand, W. M. (1971). "Objective criteria for the evaluation of clustering methods".

7233: 7228:; Sander, J.; Goebel, R. (2014). "Model Selection for Semi-Supervised Clustering". 7162: 7135: 6968: 6956: 6926: 6906: 6782: 6763: 6741: 6704: 6682: 6649: 6627: 6580: 6529: 6471: 6459: 6426: 6414: 6350: 6261: 6132: 6086: 6059: 6032: 5963: 5958: 5953: 5941: 5909: 5897: 5859: 5806: 5431: 5402: 5281: 5238: 4598: 4574: 4562: 2207: 2063: 1937: 1768: 1742: 1344: 1022: 1014: 784: 537: 487: 397: 381: 213: 208: 148: 46: 7579: 5316:

and test panels. Market researchers use cluster analysis to partition the general

11063: 10807: 10669: 10596: 10271: 10145: 10118: 10095: 10064: 9691: 9686: 9640: 9370: 9021: 8750: 8694: 8516: 8158: 8078: 6786: 6584: 6164: 5926: 5307: 5271: 5177: 4407: 4380: 3304: 3277: 1988:

parameter entirely and offering performance improvements over OPTICS by using an

1847:

While the theoretical foundation of these methods is excellent, they suffer from

1764: 1631:) are known: SLINK for single-linkage and CLINK for complete-linkage clustering. 1123: 812: 616: 482: 422: 10553: 2902:-means clustering, and is also used to determine the optimal number of clusters. 1036:

between cluster members, dense areas of the data space, intervals or particular

11012: 11007: 9470: 9400: 9046: 8724: 8689: 8679: 8504: 8262: 8088: 7970:

Arnott, Robert D. (1980-11-01). "Cluster Analysis and Stock Price Comovement".

7510: 7237: 6777:

Meilă, Marina (2003). "Comparing Clusterings by the Variation of Information".

5922: 5509: 5367: 5356: 5230: 5203: 3919:

The Jaccard index is used to quantify the similarity between two datasets. The

3466: 3445: 3441: 1396:): objects may belong to more than one cluster; usually involving hard clusters 1299: 1277: 1085: 1010: 1002: 832: 363: 100: 7881:"Determining Structural Similarity of Chemicals Using Graph Theoretic Indices" 7442: 7139: 6960: 6463: 6354: 6308: 6063: 4786:

uniformly randomly distributed data points. Now define two distance measures,

4549:. Chance normalized versions of recall, precision and G-measure correspond to 11255: 11169: 11136: 10999: 10960: 10771: 10740: 10204: 10158: 9763: 9465: 9292: 9056: 9051: 8669: 8649: 8566: 8245: 7991: 7860:

Bewley, A.; et al. "Real-time volume estimation of a dragline payload".

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Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008-07-07).

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To find weather regimes or preferred sea level pressure atmospheric patterns.

4353: 3250: 2933: 2226:" evaluation, where the clustering is summarized to a single quality score, " 2134:. With the recent need to process larger and larger data sets (also known as 1872: 1709: 994: 751: 680: 562: 293: 178: 7940: 7672: 7503:

2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542)

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The Text Mining Handbook: Advanced Approaches in Analyzing Unstructured Data

6910: 6686: 6018:"SLINK: an optimally efficient algorithm for the single-link cluster method" 4044:{\displaystyle J(A,B)={\frac {|A\cap B|}{|A\cup B|}}={\frac {TP}{TP+FP+FN}}} 2173:

of their attributes. Examples for such clustering algorithms are CLIQUE and

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University of California Publications in American Archaeology and Ethnology

5424: 5280:, cluster analysis can be used to differentiate between different types of 4550: 1375:: objects can also belong to no cluster; in which case they are considered 1269: 1220: 1119: 1115: 7983: 7571: 7427:"External clustering validity index based on chi-squared statistical test" 7023:

Weiss, Sholom M.; Indurkhya, Nitin; Zhang, Tong; Damerau, Fred J. (2005).

6745: 6631: 6341:-means algorithm for clustering large data sets with categorical values". 5901: 3879:

allocates an increasing amount of weight to recall in the final F-measure.

1445: 1406:: objects that belong to a child cluster also belong to the parent cluster 11154: 11116: 10799: 10700: 10562: 10375: 10342: 9834: 9751: 9746: 9390: 9347: 9327: 9307: 9297: 9066: 8851: 8622: 8531: 8526: 8148: 8126: 7793: 7199: 7126:

Dunn, J. (1974). "Well separated clusters and optimal fuzzy partitions".

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with related expression patterns (also known as coexpressed genes) as in

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from its nearest neighbor in X. We then define the Hopkins statistic as:

4318:{\displaystyle FM={\sqrt {{\frac {TP}{TP+FP}}\cdot {\frac {TP}{TP+FN}}}}} 3511:(both external evaluation measures in themselves) be defined as follows: 2273:-means, nor of an evaluation criterion that assumes convexity, is sound. 2170: 1848: 1735: 557: 51: 7501:

Banerjee, A. (2004). "Validating clusters using the Hopkins statistic".

7451: 6533: 6388:." In: Proc. Int'l Conf. on Management of Data, ACM SIGMOD, pp. 103–114. 6265: 6050:

Defays, D. (1977). "An efficient algorithm for a complete link method".

2066:

is a DBSCAN variant, improving handling of different densities clusters.

10000: 9480: 9180: 9111: 9061: 9036: 8956: 8745: 8704: 8699: 8612: 8521: 8429: 8341: 8321: 7826:"2022 Accelerate State of DevOps Report". 29 September 2022: 8, 14, 74. 7555: 7361: 7319: 7284: 6781:. Lecture Notes in Computer Science. Vol. 2777. pp. 173–187. 6569:. Lecture Notes in Computer Science. Vol. 4443. pp. 152–163. 6565:(2007). "Detection and Visualization of Subspace Cluster Hierarchies". 6518:. Lecture Notes in Computer Science. Vol. 4213. pp. 446–453. 6250:. Lecture Notes in Computer Science. Vol. 3918. pp. 119–128. 6186: 5968: 5317: 5114: in this section. Unsourced material may be challenged and removed. 4554: 3437: 3107: 2686: 2092:

Randomly select a cell ‘c’, where c should not be traversed beforehand.

2011: 1463: 1060:

and model parameters until the result achieves the desired properties.

991: 706: 402: 328: 7688: 7025:

Text Mining: Predictive Methods for Analyzing Unstructured Information

6816: 6726:(2007). "On Exploring Complex Relationships of Correlation Clusters". 6418: 5491:

Clustering has been used to analyse the effectiveness of DevOps teams.

1914:

Density-based clusters cannot be modeled using Gaussian distributions.

10153: 10005: 9625: 9420: 9332: 9317: 9312: 9277: 8740: 8709: 8607: 8451: 8414: 8351: 8305: 8300: 8285: 7542:

Johnson, Stephen C. (1967-09-01). "Hierarchical clustering schemes".

6219: 5863: 5810: 5384:. There are currently a number of web-based clustering tools such as 5325: 5171: 4693:

dimensional space. Consider a random sample (without replacement) of

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rate. We can calculate the F-measure by using the following formula:

3457: 3089:{\displaystyle {\frac {1}{N}}\sum _{m\in M}\max _{d\in D}{|m\cap d|}} 2868: 2082: 1717: 1276:

from the product of the signs on the edges. Under the assumptions of

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MultiClust: Discovering, Summarizing, and Using Multiple Clusterings

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Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery

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The clustering of chemical properties in different sample locations.

5198:, or genes that are co-regulated. High throughput experiments using 5142: 5089: 1863:

One prominent method is known as Gaussian mixture models (using the

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Filipovych, Roman; Resnick, Susan M.; Davatzikos, Christos (2011).

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Zubin, Joseph (1938). "A technique for measuring like-mindedness".

5321: 5277: 5264: 5245: 5211: 5190:. Often such groups contain functionally related proteins, such as 3905:

is not taken into account and can vary from 0 upward without bound.

2476: 2135: 1049: 7337:. International Conference on Cognitive Science. pp. 529–534. 7187:; Kröger, Peer; Müller, Emmanuel; Schubert, Erich; Seidl, Thomas; 11174: 10875: 8765: 8602: 8556: 8479: 8379: 8374: 8326: 7673:"High-Throughput Genotyping with Single Nucleotide Polymorphisms" 6862:"Clustering by a Genetic Algorithm with Biased Mutation Operator" 5251:

Clustering algorithms are used to automatically assign genotypes.

5161: 2214:, has led to the creation of new types of clustering algorithms. 1693: 641: 1181:: clusters are modeled using statistical distributions, such as 11096: 10077: 10051: 10031: 9282: 9073: 8780: 8760: 8632: 8424: 7210: 6667:(2004). "Computing Clusters of Correlation Connected objects". 6490:

Density-Connected Subspace Clustering for High-Dimensional Data

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does not exist a different, and maybe even better, clustering.

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Ideas from density-based clustering methods (in particular the

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The clustering framework most closely related to statistics is

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gives a formal definition as an optimization problem: find the

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Basak, S.C.; Magnuson, V.R.; Niemi, C.J.; Regal, R.R. (1988).

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Cluster analysis has been used to cluster stocks into sectors.

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defines clusters as connected dense regions in the data space.

1067:, there is a number of terms with similar meanings, including 8925: 8581: 8561: 8551: 8546: 8541: 8536: 8499: 8331: 5427: 5183: 5154: 3307:. The instances being counted here are the number of correct 1490: 1486: 636: 631: 358: 7182: 6386:

An Efficient Data Clustering Method for Very Large Databases

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works well, since it uses Gaussians for modelling clusters.

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Microsoft academic search: most cited data mining articles

5925:(May 1967) "Clustering and structural balance in graphs", 6567:

Advances in Databases: Concepts, Systems and Applications

6216:

ACM SIGMOD international conference on Management of data

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in a three-dimensional image for many different purposes.

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The F-measure can be used to balance the contribution of

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is considered the best algorithm based on this criterion.

1354:

There are also finer distinctions possible, for example:

7862:

IEEE International Conference on Robotics and Automation

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Knowledge Discovery in Databases – Part III – Clustering

6946: 6717: 6556: 6505: 6111: 5599: 4484:, while the F-measure is their harmonic mean. Moreover, 2112:

Repeat steps 2,3 and 4 till all the cells are traversed.

1964:. DeLi-Clu, Density-Link-Clustering combines ideas from 1960:, and produces a hierarchical result related to that of 1824:-medoids are special cases of the uncapacitated, metric 924:

List of datasets in computer vision and image processing

7878: 7775: 7773: 6077:

Lloyd, S. (1982). "Least squares quantization in PCM".

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of the clusters. Similarly, the intra-cluster distance

1446:

Connectivity-based clustering (hierarchical clustering)

7670: 7060: 6662: 6612:(2006). "Mining Hierarchies of Correlation Clusters". 6607: 5661: 1856:

methods include more parsimonious models based on the

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If the density of ‘c’ greater than threshold density

1974: 1946: 1597: 1547: 1507: 1126:

beginning in 1943 for trait theory classification in

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Autoregressive conditional heteroskedasticity (ARCH)

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Pourrajabi, M.; Moulavi, D.; Campello, R. J. G. B.;

7193:"On Using Class-Labels in Evaluation of Clusterings" 6514:(2006). "Finding Hierarchies of Subspace Clusters". 6176: 5694: 2008:

that are able to precisely model this kind of data.

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The most popular density-based clustering method is

7819: 7627: 6167:: DBSCAN is on rank 24, when accessed on: 4/18/2010 5769:"Quantitative Expression of Cultural Relationships" 2526:is the average distance of all elements in cluster 10300: 7730:"Semi-supervised Cluster Analysis of Imaging Data" 7261:(336). American Statistical Association: 846–850. 7178: 7176: 7152: 6397: 6291:Data Clustering : Algorithms and Applications 5766: 5052: 4898: 4865: 4838: 4805: 4778: 4758: 4738: 4711: 4685: 4665: 4645: 4541: 4511: 4472: 4452: 4425: 4398: 4371: 4344: 4317: 4208: 4133: 4110: 4073: 4043: 3897: 3871: 3851: 3821: 3788: 3758: 3658: 3634: 3610: 3557: 3491: 3424: 3349: 3326: 3295: 3268: 3241: 3218: 3191: 3088: 3002: 2982: 2962: 2811: 2668: 2641: 2614: 2565: 2538: 2518: 2491: 2467: 2432: 1980: 1952: 1623: 1579: 1533: 6245: 5143:Biology, computational biology and bioinformatics 4095:The Dice symmetric measure doubles the weight on 3416: 3403: 2851:) measures the intra-cluster distance of cluster 2104:Calculate the density of all the neighbors of ‘c’ 11253: 7155:Journal of Computational and Applied Mathematics 5938: 5733:Determining the number of clusters in a data set 3050: 2762: 2714: 2344: 2260:Determining the number of clusters in a data set 2089:Divide data space into a finite number of cells. 1899: 1170:represents each cluster by a single mean vector. 10386:Multivariate adaptive regression splines (MARS) 7779: 7385:Journal of the American Statistical Association 7300:Journal of the American Statistical Association 7254:Journal of the American Statistical Association 7173: 6248:Advances in Knowledge Discovery and Data Mining 5887: 3192:{\displaystyle RI={\frac {TP+TN}{TP+FP+FN+TN}}} 2159:clustering algorithms for high-dimensional data 2153:, many of the existing methods fail due to the 1811:-means cannot represent density-based clusters. 1734:), choosing the initial centers less randomly ( 1692:The optimization problem itself is known to be 7473: 7297: 6384:Tian Zhang, Raghu Ramakrishnan, Miron Livny. " 6289:Aggarwal, Charu C.; Reddy, Chandan K. (eds.). 2192:Several different clustering systems based on 1040:. Clustering can therefore be formulated as a 919:List of datasets for machine-learning research 8941: 8017: 6986: 6494:Proc. SIAM Int. Conf. on Data Mining (SDM'04) 6241: 6239: 5799:The Journal of Abnormal and Social Psychology 1456:Connectivity-based clustering, also known as 1155:builds models based on distance connectivity. 952: 8031: 7592: 6987:Feldman, Ronen; Sanger, James (2007-01-01). 4209:{\displaystyle DSC={\frac {2TP}{2TP+FP+FN}}} 2294:can be calculated by the following formula: 2217: 1663: 1371:Strict partitioning clustering with outliers 1365:: each object belongs to exactly one cluster 7348:Arabie, P. (1985). "Comparing partitions". 6942: 6940: 6938: 6936: 6516:Knowledge Discovery in Databases: PKDD 2006 5225:is used to group homologous sequences into 3425:{\displaystyle TP+TN+FP+FN={\binom {N}{2}}} 2835:) represents the distance between clusters 1919: 1816:Centroid-based clustering problems such as 8986: 8948: 8934: 8024: 8010: 7217: 7111:: CS1 maint: location missing publisher ( 6236: 5883: 5881: 5879: 5877: 5875: 5873: 2196:have been proposed. One is Marina Meilă's 1887:Gaussian mixture model clustering examples 1741:) or allowing a fuzzy cluster assignment ( 1501:). In the general case, the complexity is 959: 945: 9599: 7896: 7808: 7753: 7704: 7450: 7335:Recall and Precision versus the Bookmaker 7266: 6900: 6878: 6815: 6735: 6676: 6621: 6574: 6523: 6453: 6288: 6255: 6227: 6125:WIREs Data Mining and Knowledge Discovery 5967: 5957: 5852:Journal of Abnormal and Social Psychology 5301: 5130:Learn how and when to remove this message 5046: 2805: 1831: 1330:: each object belongs to a cluster or not 7500: 6933: 6859: 6058:(4). British Computer Society: 364–366. 2071: 1466:, which explains where the common name " 29: 7541: 7382: 6321: 6079:IEEE Transactions on Information Theory 5995:. Chichester, West Sussex, U.K: Wiley. 5990: 5870: 5849: 4629:There are multiple formulations of the 2076:The grid-based technique is used for a 1580:{\displaystyle {\mathcal {O}}(2^{n-1})} 1485:(the maximum of object distances), and 27:Grouping a set of objects by similarity 14: 11254: 10912:Kaplan–Meier estimator (product limit) 7969: 7409: 7347: 7332: 7326: 6049: 6031:(1). British Computer Society: 30–34. 6015: 5370:, clustering may be used to recognize 5229:. This is a very important concept in 5210: – a general aspect of 5182:Clustering is used to build groups of 3010:data points, purity can be defined as: 2906: 2253: 2119: 1706:another algorithm introduced this name 10985: 10552: 10299: 9598: 9368: 8985: 8929: 8005: 7403: 7198:. In Fern, Xiaoli Z.; Davidson, Ian; 7084: 7082: 7063:Introduction to Information Retrieval 7018: 7016: 6982: 6980: 6978: 6776: 6337:Huang, Z. (1998). "Extensions to the 6336: 6210:Ankerst, Mihael; Breunig, Markus M.; 6076: 6070: 5831: 5796: 5600:Specialized types of cluster analysis 3611:{\displaystyle R={\frac {TP}{TP+FN}}} 3558:{\displaystyle P={\frac {TP}{TP+FP}}} 2234:" evaluation by a human expert, and " 1624:{\displaystyle {\mathcal {O}}(n^{2})} 1534:{\displaystyle {\mathcal {O}}(n^{3})} 11222: 10922:Accelerated failure time (AFT) model 8862:Generative adversarial network (GAN) 7911: 7250: 7125: 6405:(July 2012). "Subspace clustering". 5502:Sequence analysis in social sciences 5112:adding citations to reliable sources 5083: 4492:are also known as Wallace's indices 3833:has no impact on the F-measure when 11234: 10517:Analysis of variance (ANOVA, anova) 9369: 6779:Learning Theory and Kernel Machines 6663:Böhm, C.; Kailing, K.; Kröger, P.; 6608:Achtert, E.; Böhm, C.; Kröger, P.; 6442:Data Mining and Knowledge Discovery 6343:Data Mining and Knowledge Discovery 5662:Techniques used in cluster analysis 5423:Clustering can be used to divide a 5401: 4846:from its nearest neighbor in X and 4633:. A typical one is as follows. Let 4610: 4433:index is the geometric mean of the 1752:-means-type algorithms require the 1481:(the minimum of object distances), 914:Glossary of artificial intelligence 24: 10612:Cochran–Mantel–Haenszel statistics 9238:Pearson product-moment correlation 7859: 7488:10.1093/oxfordjournals.aob.a083391 7383:Wallace, D. L. (1983). "Comment". 7183:Färber, Ines; Günnemann, Stephan; 7079: 7013: 6975: 5890:ACM SIGKDD Explorations Newsletter 5479:Clustering can be used to resolve 5287:Analysis of antimicrobial activity 3407: 2788: 2622:is the distance between centroids 1865:expectation-maximization algorithm 1773:Expectation-maximization algorithm 1600: 1550: 1510: 1249:, that is, a subset of nodes in a 1187:expectation-maximization algorithm 25: 11283: 7505:. Vol. 1. pp. 149–153. 6949:Knowledge and Information Systems 6860:Auffarth, B. (July 18–23, 2010). 6561:; Kröger, P.; Müller-Gorman, I.; 6510:; Kröger, P.; Müller-Gorman, I.; 5695:Data projection and preprocessing 5679:Neighbourhood components analysis 5495: 5355: 3226:is the number of true positives, 2022:Density-based clustering examples 1541:for agglomerative clustering and 1183:multivariate normal distributions 997:, used in many fields, including 11233: 11221: 11209: 11196: 11195: 10986: 8900: 8899: 8879: 7746:10.1016/j.neuroimage.2010.09.074 7482:(2). Annals Botany Co: 213–227. 5616:Clustering high-dimensional data 5459:Markov chain Monte Carlo methods 5088: 4480:, and is thus also known as the 2056: 2041: 2026: 1907: 1891: 1801: 1786: 1775:for this model discussed below. 1651: 1639: 1497:phenomenon", in particular with 10871:Least-squares spectral analysis 7963: 7905: 7872: 7853: 7721: 7664: 7621: 7586: 7535: 7494: 7467: 7418: 7376: 7341: 7291: 7244: 7146: 7119: 6872: 6853: 6803: 6770: 6711: 6656: 6601: 6550: 6499: 6478: 6433: 6391: 6378: 6369: 6330: 6315: 6282: 6203: 6170: 6151: 6105: 6043: 5606:Automatic clustering algorithms 5099:needs additional citations for 5079: 1708:). It does however only find a 9852:Mean-unbiased minimum-variance 8955: 8812:Recurrent neural network (RNN) 8802:Differentiable neural computer 7912:Huth, R.; et al. (2008). 7595:Information Processing Letters 7397:10.1080/01621459.1983.10478009 7312:10.1080/01621459.1983.10478008 7065:. Cambridge University Press. 6115:; Kröger, Peer; Sander, Jörg; 6009: 5984: 5959:10.1016/j.psychres.2023.115265 5932: 5916: 5843: 5825: 5790: 5760: 5374:within large groups of people. 5149:Distance matrices in phylogeny 3993: 3979: 3972: 3958: 3948: 3936: 3714: 3695: 3081: 3067: 2799: 2793: 2756: 2744: 2615:{\displaystyle d(c_{i},c_{j})} 2609: 2583: 2420: 2394: 2101:Mark cell ‘c’ as a new cluster 2033:Density-based clustering with 1898:On Gaussian-distributed data, 1618: 1605: 1574: 1555: 1528: 1515: 1361:Strict partitioning clustering 1312:Independent Component Analysis 334:Relevance vector machine (RVM) 13: 1: 11165:Geographic information system 10381:Simultaneous equations models 8857:Variational autoencoder (VAE) 8817:Long short-term memory (LSTM) 8084:Computational learning theory 7607:10.1016/S0020-0190(00)00142-3 5753: 5237:in general. See evolution by 4592:Normalized mutual information 2855:. The inter-cluster distance 1700:, often just referred to as " 1436:list of statistics algorithms 1422: 1133: 1122:in 1939 and famously used by 990:, and a common technique for 823:Computational learning theory 387:Expectation–maximization (EM) 10348:Coefficient of determination 9959:Uniformly most powerful test 8837:Convolutional neural network 7898:10.1016/0166-218x(88)90004-2 7630:Journal of Molecular Biology 7167:10.1016/0377-0427(87)90125-7 6787:10.1007/978-3-540-45167-9_14 6585:10.1007/978-3-540-71703-4_15 6324:Web-scale k-means clustering 5706:Principal component analysis 3492:{\displaystyle \beta \geq 0} 2095:Calculate the density of ‘c’ 1981:{\displaystyle \varepsilon } 1968:and OPTICS, eliminating the 1953:{\displaystyle \varepsilon } 1308:Principal Component Analysis 1042:multi-objective optimization 780:Coefficient of determination 627:Convolutional neural network 339:Support vector machine (SVM) 7: 10917:Proportional hazards models 10861:Spectral density estimation 10843:Vector autoregression (VAR) 10277:Maximum posterior estimator 9509:Randomized controlled trial 8832:Multilayer perceptron (MLP) 5767:Driver and Kroeber (1932). 5594: 5475:Natural language processing 5340:and selecting test markets. 5263: 5206:can be a powerful tool for 2519:{\displaystyle \sigma _{i}} 2448:is the number of clusters, 1635:Linkage clustering examples 1483:complete linkage clustering 1429:Cluster analysis algorithms 931:Outline of machine learning 828:Empirical risk minimization 10: 11288: 10677:Multivariate distributions 9097:Average absolute deviation 8908:Artificial neural networks 8822:Gated recurrent unit (GRU) 8048:Differentiable programming 7972:Financial Analysts Journal 7511:10.1109/FUZZY.2004.1375706 6121:"Density-based Clustering" 5430:into distinct regions for 5343:Grouping of shopping items 5146: 4899:{\displaystyle x_{i}\in X} 4839:{\displaystyle y_{i}\in Y} 4081:is not taken into account. 2257: 2206:, a recent development in 1880:correlation and dependence 1782:-means clustering examples 1667: 1449: 1426: 568:Feedforward neural network 319:Artificial neural networks 11191: 11145: 11082: 11035: 10998: 10994: 10981: 10953: 10935: 10902: 10893: 10851: 10798: 10759: 10708: 10699: 10665:Structural equation model 10620: 10577: 10573: 10548: 10507: 10473: 10427: 10394: 10356: 10323: 10319: 10295: 10235: 10144: 10063: 10027: 10018: 10001:Score/Lagrange multiplier 9986: 9939: 9884: 9810: 9801: 9611: 9607: 9594: 9553: 9527: 9479: 9434: 9416:Sample size determination 9381: 9377: 9364: 9268: 9223: 9197: 9179: 9135: 9087: 9007: 8998: 8994: 8981: 8963: 8875: 8789: 8733: 8662: 8595: 8467: 8367: 8360: 8314: 8278: 8241:Artificial neural network 8221: 8097: 8064:Automatic differentiation 8037: 7782:Computational Linguistics 7443:10.1016/j.ins.2019.02.046 7350:Journal of Classification 7140:10.1080/01969727408546059 6991:. Cambridge Univ. Press. 6961:10.1007/s10115-008-0150-6 6464:10.1007/s10618-005-1396-1 5723:Cluster-weighted modeling 5668:Artificial neural network 5533: 4719:data points with members 2218:Evaluation and assessment 2016:kernel density estimation 1966:single-linkage clustering 1826:facility location problem 1664:Centroid-based clustering 1499:single-linkage clustering 1479:single-linkage clustering 1089: 1038:statistical distributions 988:exploratory data analysis 551:Artificial neural network 11160:Environmental statistics 10682:Elliptical distributions 10475:Generalized linear model 10404:Simple linear regression 10174:Hodges–Lehmann estimator 9631:Probability distribution 9540:Stochastic approximation 9102:Coefficient of variation 8069:Neuromorphic engineering 8032:Differentiable computing 7238:10.5441/002/edbt.2014.31 6955:(3). Springer: 361–394. 6091:10.1109/TIT.1982.1056489 5743:Structured data analysis 5716: 5711:Multidimensional scaling 5255:Human genetic clustering 5188:HCS clustering algorithm 3852:{\displaystyle \beta =0} 3789:{\displaystyle \beta =0} 2970:and some set of classes 2199:variation of information 1920:Density-based clustering 1858:eigenvalue decomposition 1256:HCS clustering algorithm 860:Journals and conferences 807:Mathematical foundations 717:Temporal difference (TD) 573:Recurrent neural network 493:Conditional random field 416:Dimensionality reduction 164:Dimensionality reduction 126:Quantum machine learning 121:Neuromorphic engineering 81:Self-supervised learning 76:Semi-supervised learning 10820:Cross-correlation (XCF) 10428:Non-standard predictors 9862:Lehmann–Scheffé theorem 9535:Adaptive clinical trial 8842:Residual neural network 8258:Artificial Intelligence 7941:10.1196/annals.1446.019 6911:10.1126/science.1136800 6718:Achtert, E.; Bohm, C.; 6687:10.1145/1007568.1007620 6557:Achtert, E.; Böhm, C.; 6506:Achtert, E.; Böhm, C.; 6355:10.1023/A:1009769707641 6064:10.1093/comjnl/20.4.364 5991:Everitt, Brian (2011). 5728:Curse of dimensionality 5674:Nearest neighbor search 5519:Educational data mining 5442:Evolutionary algorithms 5391:Slippy map optimization 5363:Social network analysis 5338:new product development 5200:expressed sequence tags 5170:to generate artificial 4561:and relate strongly to 3822:{\displaystyle F_{0}=P} 2921:. Additionally, from a 2155:curse of dimensionality 1468:hierarchical clustering 1459:hierarchical clustering 1452:Hierarchical clustering 1402:Hierarchical clustering 1153:hierarchical clustering 269:Apprenticeship learning 11216:Mathematics portal 11037:Engineering statistics 10945:Nelson–Aalen estimator 10522:Analysis of covariance 10409:Ordinary least squares 10333:Pearson product-moment 9737:Statistical functional 9648:Empirical distribution 9481:Controlled experiments 9210:Frequency distribution 8988:Descriptive statistics 7839:Cite journal requires 7642:10.1006/jmbi.2000.5197 7412:The Problem with Kappa 7410:Powers, David (2012). 7333:Powers, David (2003). 7128:Journal of Cybernetics 6841:Cite journal requires 6037:10.1093/comjnl/16.1.30 5641:Data stream clustering 5631:Constrained clustering 5548:Mathematical chemistry 5377:Search result grouping 5302:Business and marketing 5054: 5025: 4984: 4944: 4900: 4873:to be the distance of 4867: 4840: 4813:to be the distance of 4807: 4780: 4760: 4746:. Also generate a set 4740: 4713: 4712:{\displaystyle m\ll n} 4687: 4667: 4647: 4543: 4542:{\displaystyle B^{II}} 4513: 4474: 4454: 4427: 4400: 4373: 4346: 4319: 4210: 4135: 4112: 4075: 4045: 3899: 3873: 3872:{\displaystyle \beta } 3853: 3823: 3790: 3760: 3660: 3636: 3612: 3559: 3493: 3426: 3351: 3328: 3311:assignments. That is, 3297: 3270: 3243: 3220: 3193: 3090: 3004: 2984: 2964: 2927:constrained clustering 2890:Silhouette coefficient 2813: 2670: 2643: 2616: 2567: 2540: 2520: 2493: 2469: 2434: 2342: 2167:correlation clustering 1982: 1954: 1869:Gaussian distributions 1854:model-based clustering 1838:model-based clustering 1832:Model-based clustering 1625: 1581: 1535: 1390:alternative clustering 1384:Overlapping clustering 1295:: the most well-known 1128:personality psychology 818:Bias–variance tradeoff 700:Reinforcement learning 676:Spiking neural network 86:Reinforcement learning 35: 11132:Population statistics 11074:System identification 10808:Autocorrelation (ACF) 10736:Exponential smoothing 10650:Discriminant analysis 10645:Canonical correlation 10509:Partition of variance 10371:Regression validation 10215:(Jonckheere–Terpstra) 10114:Likelihood-ratio test 9803:Frequentist inference 9715:Location–scale family 9636:Sampling distribution 9601:Statistical inference 9568:Cross-sectional study 9555:Observational studies 9514:Randomized experiment 9343:Stem-and-leaf display 9145:Central limit theorem 8797:Neural Turing machine 8385:Human image synthesis 7984:10.2469/faj.v36.n6.56 7099:Heidelberg University 6746:10.1109/SSDBM.2007.21 6632:10.1109/SSDBM.2006.35 5902:10.1145/568574.568575 5684:Latent class analysis 5621:Conceptual clustering 5055: 5005: 4964: 4924: 4901: 4868: 4866:{\displaystyle w_{i}} 4841: 4808: 4806:{\displaystyle u_{i}} 4781: 4761: 4741: 4739:{\displaystyle x_{i}} 4714: 4688: 4668: 4648: 4588:information theoretic 4575:chi-squared statistic 4544: 4514: 4512:{\displaystyle B^{I}} 4475: 4455: 4428: 4401: 4374: 4347: 4320: 4224:Fowlkes–Mallows index 4211: 4136: 4118:while still ignoring 4113: 4076: 4046: 3900: 3874: 3854: 3824: 3791: 3761: 3661: 3637: 3613: 3560: 3494: 3427: 3352: 3329: 3298: 3271: 3244: 3221: 3194: 3091: 3005: 2985: 2965: 2814: 2671: 2669:{\displaystyle c_{j}} 2644: 2642:{\displaystyle c_{i}} 2617: 2568: 2566:{\displaystyle c_{i}} 2541: 2521: 2494: 2470: 2468:{\displaystyle c_{i}} 2435: 2322: 2151:high-dimensional data 2072:Grid-based clustering 1983: 1955: 1626: 1582: 1536: 1394:multi-view clustering 1007:information retrieval 654:Neural radiance field 476:Structured prediction 199:Structured prediction 71:Unsupervised learning 33: 11055:Probabilistic design 10640:Principal components 10483:Exponential families 10435:Nonlinear regression 10414:General linear model 10376:Mixed effects models 10366:Errors and residuals 10343:Confounding variable 10245:Bayesian probability 10223:Van der Waerden test 10213:Ordered alternative 9978:Multiple comparisons 9857:Rao–Blackwellization 9820:Estimating equations 9776:Statistical distance 9494:Factorial experiment 9027:Arithmetic-Geometric 8888:Computer programming 8867:Graph neural network 8442:Text-to-video models 8420:Text-to-image models 8268:Large language model 8253:Scientific computing 8059:Statistical manifold 8054:Information geometry 7794:10.1162/COLI_a_00148 7431:Information Sciences 7232:. pp. 331–342. 6616:. pp. 119–128. 6496:, pp. 246–257, 2004. 6322:Sculley, D. (2010). 6189:. pp. 226–231. 6052:The Computer Journal 6025:The Computer Journal 5738:Parallel coordinates 5689:Affinity propagation 5626:Consensus clustering 5235:evolutionary biology 5108:improve this article 4912: 4877: 4850: 4817: 4790: 4770: 4750: 4723: 4697: 4677: 4657: 4637: 4559:Matthews Correlation 4523: 4496: 4464: 4444: 4414: 4387: 4360: 4333: 4238: 4147: 4122: 4099: 4062: 3930: 3886: 3863: 3837: 3800: 3774: 3676: 3650: 3626: 3570: 3517: 3477: 3473:through a parameter 3361: 3338: 3315: 3284: 3257: 3230: 3207: 3121: 3020: 2994: 2990:, both partitioning 2974: 2954: 2701: 2678:Davies–Bouldin index 2653: 2626: 2577: 2550: 2530: 2503: 2483: 2452: 2300: 2292:Davies–Bouldin index 2283:Davies–Bouldin index 1995:The key drawback of 1972: 1944: 1840:, which is based on 1595: 1545: 1505: 1103:typological analysis 843:Statistical learning 741:Learning with humans 533:Local outlier factor 11127:Official statistics 11050:Methods engineering 10731:Seasonal adjustment 10499:Poisson regressions 10419:Bayesian regression 10358:Regression analysis 10338:Partial correlation 10310:Regression analysis 9909:Prediction interval 9904:Likelihood interval 9894:Confidence interval 9886:Interval estimation 9847:Unbiased estimators 9665:Model specification 9545:Up-and-down designs 9233:Partial correlation 9189:Index of dispersion 9107:Interquartile range 8234:In-context learning 8074:Pattern recognition 7933:2008NYASA1146..105H 7921:Ann. N.Y. Acad. Sci 7185:Kriegel, Hans-Peter 6893:2007Sci...315..972F 6826:2003q.bio....11039K 6534:10.1007/11871637_42 6399:Kriegel, Hans-Peter 6266:10.1007/11731139_16 6212:Kriegel, Hans-Peter 6179:Kriegel, Hans-Peter 6113:Kriegel, Hans-Peter 6016:Sibson, R. (1973). 5946:Psychiatry Research 5839:. Edwards Brothers. 5748:Linear separability 5701:Dimension reduction 5656:Spectral clustering 5651:Sequence clustering 5636:Community detection 5611:Balanced clustering 5554:topological indices 5450:Recommender systems 5334:product positioning 5330:market segmentation 5223:Sequence clustering 5041: 5000: 4960: 3450:adjusted Rand index 3436:One issue with the 2923:knowledge discovery 2907:External evaluation 2254:Internal evaluation 2212:statistical physics 2163:subspace clustering 2120:Recent developments 1842:distribution models 1732:-medians clustering 1589:divisive clustering 1413:Subspace clustering 1304:self-organizing map 1262:Signed graph models 1166:: for example, the 1108:community detection 1054:knowledge discovery 999:pattern recognition 686:Electrochemical RAM 593:reservoir computing 324:Logistic regression 243:Supervised learning 229:Multimodal learning 204:Feature engineering 149:Generative modeling 111:Rule-based learning 106:Curriculum learning 66:Supervised learning 41:Part of a series on 11147:Spatial statistics 11027:Medical statistics 10927:First hitting time 10881:Whittle likelihood 10532:Degrees of freedom 10527:Multivariate ANOVA 10460:Heteroscedasticity 10272:Bayesian estimator 10237:Bayesian inference 10086:Kolmogorov–Smirnov 9971:Randomization test 9941:Testing hypotheses 9914:Tolerance interval 9825:Maximum likelihood 9720:Exponential family 9653:Density estimation 9613:Statistical theory 9573:Natural experiment 9519:Scientific control 9436:Survey methodology 9122:Standard deviation 8827:Echo state network 8715:Jürgen Schmidhuber 8410:Facial recognition 8405:Speech recognition 8315:Software libraries 7556:10.1007/BF02289588 7362:10.1007/BF01908075 6486:Hans-Peter Kriegel 6222:. pp. 49–60. 6163:2010-04-21 at the 5436:object recognition 5419:Image segmentation 5410:Software evolution 5071:distribution, not 5050: 5027: 4986: 4946: 4896: 4863: 4836: 4803: 4776: 4756: 4736: 4709: 4683: 4663: 4643: 4583:mutual information 4539: 4509: 4470: 4450: 4426:{\displaystyle FM} 4423: 4399:{\displaystyle FN} 4396: 4372:{\displaystyle FP} 4369: 4345:{\displaystyle TP} 4342: 4315: 4206: 4134:{\displaystyle TN} 4131: 4111:{\displaystyle TP} 4108: 4074:{\displaystyle TN} 4071: 4041: 3898:{\displaystyle TN} 3895: 3869: 3849: 3829:. In other words, 3819: 3786: 3756: 3656: 3632: 3608: 3555: 3489: 3422: 3350:{\displaystyle FP} 3347: 3327:{\displaystyle TP} 3324: 3296:{\displaystyle FN} 3293: 3269:{\displaystyle FP} 3266: 3242:{\displaystyle TN} 3239: 3219:{\displaystyle TP} 3216: 3189: 3086: 3064: 3048: 3000: 2980: 2960: 2809: 2782: 2740: 2666: 2639: 2612: 2563: 2536: 2516: 2489: 2465: 2430: 2358: 2204:belief propagation 2194:mutual information 2144:k-means clustering 1978: 1962:linkage clustering 1950: 1754:number of clusters 1670:k-means clustering 1621: 1577: 1531: 1475:distance functions 1176:Distribution model 1146:Connectivity model 1077:numerical taxonomy 1058:data preprocessing 254: • 169:Density estimation 36: 11249: 11248: 11187: 11186: 11183: 11182: 11122:National accounts 11092:Actuarial science 11084:Social statistics 10977: 10976: 10973: 10972: 10969: 10968: 10904:Survival function 10889: 10888: 10751:Granger causality 10592:Contingency table 10567:Survival analysis 10544: 10543: 10540: 10539: 10396:Linear regression 10291: 10290: 10287: 10286: 10262:Credible interval 10231: 10230: 10014: 10013: 9830:Method of moments 9699:Parametric family 9660:Statistical model 9590: 9589: 9586: 9585: 9504:Random assignment 9426:Statistical power 9360: 9359: 9356: 9355: 9205:Contingency table 9175: 9174: 9042:Generalized/power 8923: 8922: 8685:Stephen Grossberg 8658: 8657: 7885:Discr. Appl. Math 7689:10.1101/gr.157801 7520:978-0-7803-8353-1 7072:978-0-521-86571-5 6887:(5814): 972–976. 6796:978-3-540-40720-1 6755:978-0-7695-2868-7 6641:978-0-7695-2590-7 6594:978-3-540-71702-7 6543:978-3-540-45374-1 6488:and Peer Kröger. 6419:10.1002/widm.1057 6326:. Proc. 19th WWW. 6300:978-1-315-37351-5 6275:978-3-540-33206-0 5579:Petroleum geology 5481:lexical ambiguity 5467:Anomaly detection 5328:, and for use in 5294:IMRT segmentation 5218:Sequence analysis 5208:genome annotation 5168:plant systematics 5140: 5139: 5132: 5044: 4779:{\displaystyle m} 4759:{\displaystyle Y} 4686:{\displaystyle d} 4666:{\displaystyle n} 4646:{\displaystyle X} 4631:Hopkins statistic 4622:Hopkins statistic 4473:{\displaystyle R} 4453:{\displaystyle P} 4406:is the number of 4379:is the number of 4352:is the number of 4313: 4311: 4279: 4204: 4039: 3998: 3859:, and increasing 3754: 3659:{\displaystyle R} 3635:{\displaystyle P} 3606: 3553: 3414: 3303:is the number of 3276:is the number of 3249:is the number of 3187: 3049: 3033: 3031: 3003:{\displaystyle N} 2983:{\displaystyle D} 2963:{\displaystyle M} 2803: 2761: 2713: 2539:{\displaystyle i} 2492:{\displaystyle i} 2424: 2343: 2320: 2140:canopy clustering 2078:multi-dimensional 1702:k-means algorithm 1698:Lloyd's algorithm 1683:-means clustering 1240:Graph-based model 1168:k-means algorithm 1063:Besides the term 1046:distance function 1019:computer graphics 969: 968: 774:Model diagnostics 757:Human-in-the-loop 600:Boltzmann machine 513:Anomaly detection 309:Linear regression 224:Ontology learning 219:Grammar induction 194:Semantic analysis 189:Association rules 174:Anomaly detection 116:Neuro-symbolic AI 16:(Redirected from 11279: 11262:Cluster analysis 11237: 11236: 11225: 11224: 11214: 11213: 11199: 11198: 11102:Crime statistics 10996: 10995: 10983: 10982: 10900: 10899: 10866:Fourier analysis 10853:Frequency domain 10833: 10780: 10746:Structural break 10706: 10705: 10655:Cluster analysis 10602:Log-linear model 10575: 10574: 10550: 10549: 10491: 10465:Homoscedasticity 10321: 10320: 10297: 10296: 10216: 10208: 10200: 10199:(Kruskal–Wallis) 10184: 10169: 10124:Cross validation 10109: 10091:Anderson–Darling 10038: 10025: 10024: 9996:Likelihood-ratio 9988:Parametric tests 9966:Permutation test 9949:1- & 2-tails 9840:Minimum distance 9812:Point estimation 9808: 9807: 9759:Optimal decision 9710: 9609: 9608: 9596: 9595: 9578:Quasi-experiment 9528:Adaptive designs 9379: 9378: 9366: 9365: 9243:Rank correlation 9005: 9004: 8996: 8995: 8983: 8982: 8950: 8943: 8936: 8927: 8926: 8913:Machine learning 8903: 8902: 8883: 8638:Action selection 8628:Self-driving car 8435:Stable Diffusion 8400:Speech synthesis 8365: 8364: 8229:Machine learning 8105:Gradient descent 8026: 8019: 8012: 8003: 8002: 7996: 7995: 7967: 7961: 7960: 7918: 7909: 7903: 7902: 7900: 7876: 7870: 7869: 7857: 7851: 7848: 7842: 7837: 7835: 7827: 7823: 7817: 7812: 7806: 7805: 7777: 7768: 7767: 7757: 7740:(3): 2185–2197. 7725: 7719: 7718: 7708: 7683:(7): 1262–1268. 7668: 7662: 7661: 7636:(5): 1041–1052. 7625: 7619: 7618: 7590: 7584: 7583: 7539: 7533: 7532: 7498: 7492: 7491: 7476:Annals of Botany 7471: 7465: 7464: 7454: 7422: 7416: 7415: 7407: 7401: 7400: 7391:(383): 569–579. 7380: 7374: 7373: 7345: 7339: 7338: 7330: 7324: 7323: 7306:(383): 553–569. 7295: 7289: 7288: 7270: 7248: 7242: 7241: 7221: 7215: 7214: 7197: 7180: 7171: 7170: 7150: 7144: 7143: 7123: 7117: 7116: 7110: 7102: 7096: 7086: 7077: 7076: 7058: 7047: 7046: 7020: 7011: 7010: 6984: 6973: 6972: 6944: 6931: 6930: 6904: 6876: 6870: 6869: 6857: 6851: 6850: 6844: 6839: 6837: 6829: 6819: 6807: 6801: 6800: 6774: 6768: 6767: 6739: 6715: 6709: 6708: 6680: 6660: 6654: 6653: 6625: 6605: 6599: 6598: 6578: 6554: 6548: 6547: 6527: 6503: 6497: 6482: 6476: 6475: 6457: 6437: 6431: 6430: 6401:; Kröger, Peer; 6395: 6389: 6382: 6376: 6373: 6367: 6366: 6334: 6328: 6327: 6319: 6313: 6312: 6286: 6280: 6279: 6259: 6243: 6234: 6233: 6231: 6207: 6201: 6200: 6174: 6168: 6155: 6149: 6148: 6109: 6103: 6102: 6074: 6068: 6067: 6047: 6041: 6040: 6022: 6013: 6007: 6006: 5993:Cluster analysis 5988: 5982: 5981: 5971: 5961: 5936: 5930: 5920: 5914: 5913: 5885: 5868: 5867: 5864:10.1037/h0054116 5847: 5841: 5840: 5833:Tryon, Robert C. 5829: 5823: 5822: 5811:10.1037/h0055441 5794: 5788: 5787: 5785: 5784: 5764: 5432:border detection 5403:Computer science 5366:In the study of 5244:High-throughput 5239:gene duplication 5135: 5128: 5124: 5121: 5115: 5092: 5084: 5059: 5057: 5056: 5051: 5045: 5043: 5042: 5040: 5035: 5024: 5019: 5001: 4999: 4994: 4983: 4978: 4962: 4961: 4959: 4954: 4943: 4938: 4922: 4905: 4903: 4902: 4897: 4889: 4888: 4872: 4870: 4869: 4864: 4862: 4861: 4845: 4843: 4842: 4837: 4829: 4828: 4812: 4810: 4809: 4804: 4802: 4801: 4785: 4783: 4782: 4777: 4765: 4763: 4762: 4757: 4745: 4743: 4742: 4737: 4735: 4734: 4718: 4716: 4715: 4710: 4692: 4690: 4689: 4684: 4672: 4670: 4669: 4664: 4652: 4650: 4649: 4644: 4611:Cluster tendency 4599:Confusion matrix 4548: 4546: 4545: 4540: 4538: 4537: 4518: 4516: 4515: 4510: 4508: 4507: 4479: 4477: 4476: 4471: 4459: 4457: 4456: 4451: 4432: 4430: 4429: 4424: 4405: 4403: 4402: 4397: 4378: 4376: 4375: 4370: 4351: 4349: 4348: 4343: 4324: 4322: 4321: 4316: 4314: 4312: 4310: 4293: 4285: 4280: 4278: 4261: 4253: 4251: 4215: 4213: 4212: 4207: 4205: 4203: 4174: 4163: 4140: 4138: 4137: 4132: 4117: 4115: 4114: 4109: 4080: 4078: 4077: 4072: 4050: 4048: 4047: 4042: 4040: 4038: 4012: 4004: 3999: 3997: 3996: 3982: 3976: 3975: 3961: 3955: 3904: 3902: 3901: 3896: 3878: 3876: 3875: 3870: 3858: 3856: 3855: 3850: 3828: 3826: 3825: 3820: 3812: 3811: 3795: 3793: 3792: 3787: 3765: 3763: 3762: 3757: 3755: 3753: 3740: 3739: 3729: 3707: 3706: 3693: 3688: 3687: 3665: 3663: 3662: 3657: 3641: 3639: 3638: 3633: 3617: 3615: 3614: 3609: 3607: 3605: 3588: 3580: 3564: 3562: 3561: 3556: 3554: 3552: 3535: 3527: 3498: 3496: 3495: 3490: 3431: 3429: 3428: 3423: 3421: 3420: 3419: 3406: 3356: 3354: 3353: 3348: 3333: 3331: 3330: 3325: 3302: 3300: 3299: 3294: 3275: 3273: 3272: 3267: 3248: 3246: 3245: 3240: 3225: 3223: 3222: 3217: 3198: 3196: 3195: 3190: 3188: 3186: 3151: 3134: 3095: 3093: 3092: 3087: 3085: 3084: 3070: 3063: 3047: 3032: 3024: 3009: 3007: 3006: 3001: 2989: 2987: 2986: 2981: 2969: 2967: 2966: 2961: 2912:thought of as a 2818: 2816: 2815: 2810: 2804: 2802: 2792: 2791: 2781: 2759: 2739: 2711: 2675: 2673: 2672: 2667: 2665: 2664: 2648: 2646: 2645: 2640: 2638: 2637: 2621: 2619: 2618: 2613: 2608: 2607: 2595: 2594: 2572: 2570: 2569: 2564: 2562: 2561: 2545: 2543: 2542: 2537: 2525: 2523: 2522: 2517: 2515: 2514: 2498: 2496: 2495: 2490: 2474: 2472: 2471: 2466: 2464: 2463: 2439: 2437: 2436: 2431: 2429: 2425: 2423: 2419: 2418: 2406: 2405: 2389: 2388: 2387: 2375: 2374: 2364: 2357: 2341: 2336: 2321: 2313: 2208:computer science 2060: 2045: 2030: 1987: 1985: 1984: 1979: 1959: 1957: 1956: 1951: 1911: 1901: 1895: 1805: 1790: 1769:machine learning 1655: 1643: 1630: 1628: 1627: 1622: 1617: 1616: 1604: 1603: 1586: 1584: 1583: 1578: 1573: 1572: 1554: 1553: 1540: 1538: 1537: 1532: 1527: 1526: 1514: 1513: 1416: 1415: 1404: 1403: 1386: 1385: 1373: 1372: 1363: 1362: 1348: 1347: 1345:fuzzy clustering 1338: 1337: 1328: 1327: 1292: 1291: 1242: 1241: 1231: 1230: 1216: 1215: 1197: 1196: 1178: 1177: 1163: 1162: 1148: 1147: 1100: 1097: 1094: 1091: 1023:machine learning 1015:data compression 972:Cluster analysis 961: 954: 947: 908:Related articles 785:Confusion matrix 538:Isolation forest 483:Graphical models 262: 261: 214:Learning to rank 209:Feature learning 47:Machine learning 38: 37: 21: 11287: 11286: 11282: 11281: 11280: 11278: 11277: 11276: 11252: 11251: 11250: 11245: 11208: 11179: 11141: 11078: 11064:quality control 11031: 11013:Clinical trials 10990: 10965: 10949: 10937:Hazard function 10931: 10885: 10847: 10831: 10794: 10790:Breusch–Godfrey 10778: 10755: 10695: 10670:Factor analysis 10616: 10597:Graphical model 10569: 10536: 10503: 10489: 10469: 10423: 10390: 10352: 10315: 10314: 10283: 10227: 10214: 10206: 10198: 10182: 10167: 10146:Rank statistics 10140: 10119:Model selection 10107: 10065:Goodness of fit 10059: 10036: 10010: 9982: 9935: 9880: 9869:Median unbiased 9797: 9708: 9641:Order statistic 9603: 9582: 9549: 9523: 9475: 9430: 9373: 9371:Data collection 9352: 9264: 9219: 9193: 9171: 9131: 9083: 9000:Continuous data 8990: 8977: 8959: 8954: 8924: 8919: 8871: 8785: 8751:Google DeepMind 8729: 8695:Geoffrey Hinton 8654: 8591: 8517:Project Debater 8463: 8361:Implementations 8356: 8310: 8274: 8217: 8159:Backpropagation 8093: 8079:Tensor calculus 8033: 8030: 8000: 7999: 7968: 7964: 7916: 7910: 7906: 7877: 7873: 7858: 7854: 7840: 7838: 7829: 7828: 7825: 7824: 7820: 7813: 7809: 7778: 7771: 7726: 7722: 7677:Genome Research 7669: 7665: 7626: 7622: 7591: 7587: 7540: 7536: 7521: 7499: 7495: 7472: 7468: 7423: 7419: 7408: 7404: 7381: 7377: 7346: 7342: 7331: 7327: 7296: 7292: 7277:10.2307/2284239 7249: 7245: 7222: 7218: 7195: 7181: 7174: 7151: 7147: 7124: 7120: 7104: 7103: 7094: 7088: 7087: 7080: 7073: 7059: 7050: 7035: 7021: 7014: 6999: 6985: 6976: 6945: 6934: 6902:10.1.1.121.3145 6877: 6873: 6858: 6854: 6842: 6840: 6831: 6830: 6808: 6804: 6797: 6775: 6771: 6756: 6716: 6712: 6697: 6671:. p. 455. 6661: 6657: 6642: 6623:10.1.1.707.7872 6606: 6602: 6595: 6555: 6551: 6544: 6525:10.1.1.705.2956 6504: 6500: 6484:Karin Kailing, 6483: 6479: 6455:10.1.1.131.5152 6438: 6434: 6396: 6392: 6383: 6379: 6374: 6370: 6335: 6331: 6320: 6316: 6301: 6287: 6283: 6276: 6244: 6237: 6229:10.1.1.129.6542 6208: 6204: 6197: 6177:Ester, Martin; 6175: 6171: 6165:Wayback Machine 6156: 6152: 6137:10.1002/widm.30 6110: 6106: 6075: 6071: 6048: 6044: 6020: 6014: 6010: 6003: 5989: 5985: 5937: 5933: 5927:Human Relations 5921: 5917: 5886: 5871: 5848: 5844: 5830: 5826: 5795: 5791: 5782: 5780: 5765: 5761: 5756: 5719: 5697: 5664: 5602: 5597: 5536: 5498: 5406: 5368:social networks 5360: 5308:Market research 5304: 5272:Medical imaging 5268: 5204:DNA microarrays 5194:for a specific 5178:Transcriptomics 5151: 5145: 5136: 5125: 5119: 5116: 5105: 5093: 5082: 5036: 5031: 5026: 5020: 5009: 4995: 4990: 4985: 4979: 4968: 4963: 4955: 4950: 4945: 4939: 4928: 4923: 4921: 4913: 4910: 4909: 4884: 4880: 4878: 4875: 4874: 4857: 4853: 4851: 4848: 4847: 4824: 4820: 4818: 4815: 4814: 4797: 4793: 4791: 4788: 4787: 4771: 4768: 4767: 4751: 4748: 4747: 4730: 4726: 4724: 4721: 4720: 4698: 4695: 4694: 4678: 4675: 4674: 4673:data points in 4658: 4655: 4654: 4638: 4635: 4634: 4613: 4530: 4526: 4524: 4521: 4520: 4503: 4499: 4497: 4494: 4493: 4465: 4462: 4461: 4445: 4442: 4441: 4415: 4412: 4411: 4408:false negatives 4388: 4385: 4384: 4381:false positives 4361: 4358: 4357: 4334: 4331: 4330: 4294: 4286: 4284: 4262: 4254: 4252: 4250: 4239: 4236: 4235: 4175: 4164: 4162: 4148: 4145: 4144: 4123: 4120: 4119: 4100: 4097: 4096: 4063: 4060: 4059: 4013: 4005: 4003: 3992: 3978: 3977: 3971: 3957: 3956: 3954: 3931: 3928: 3927: 3887: 3884: 3883: 3864: 3861: 3860: 3838: 3835: 3834: 3807: 3803: 3801: 3798: 3797: 3775: 3772: 3771: 3735: 3731: 3730: 3702: 3698: 3694: 3692: 3683: 3679: 3677: 3674: 3673: 3651: 3648: 3647: 3627: 3624: 3623: 3589: 3581: 3579: 3571: 3568: 3567: 3536: 3528: 3526: 3518: 3515: 3514: 3478: 3475: 3474: 3467:false negatives 3446:false negatives 3442:false positives 3415: 3402: 3401: 3400: 3362: 3359: 3358: 3339: 3336: 3335: 3316: 3313: 3312: 3305:false negatives 3285: 3282: 3281: 3278:false positives 3258: 3255: 3254: 3231: 3228: 3227: 3208: 3205: 3204: 3152: 3135: 3133: 3122: 3119: 3118: 3080: 3066: 3065: 3053: 3037: 3023: 3021: 3018: 3017: 2995: 2992: 2991: 2975: 2972: 2971: 2955: 2952: 2951: 2909: 2787: 2783: 2765: 2760: 2717: 2712: 2710: 2702: 2699: 2698: 2660: 2656: 2654: 2651: 2650: 2633: 2629: 2627: 2624: 2623: 2603: 2599: 2590: 2586: 2578: 2575: 2574: 2557: 2553: 2551: 2548: 2547: 2531: 2528: 2527: 2510: 2506: 2504: 2501: 2500: 2484: 2481: 2480: 2459: 2455: 2453: 2450: 2449: 2414: 2410: 2401: 2397: 2390: 2383: 2379: 2370: 2366: 2365: 2363: 2359: 2347: 2337: 2326: 2312: 2301: 2298: 2297: 2262: 2256: 2220: 2122: 2074: 2067: 2061: 2052: 2046: 2037: 2031: 1973: 1970: 1969: 1945: 1942: 1941: 1922: 1915: 1912: 1903: 1896: 1834: 1812: 1806: 1797: 1791: 1765:Voronoi diagram 1672: 1666: 1659: 1656: 1647: 1644: 1612: 1608: 1599: 1598: 1596: 1593: 1592: 1562: 1558: 1549: 1548: 1546: 1543: 1542: 1522: 1518: 1509: 1508: 1506: 1503: 1502: 1454: 1448: 1431: 1427:Main category: 1425: 1411: 1410: 1401: 1400: 1383: 1382: 1370: 1369: 1360: 1359: 1343: 1342: 1336:Soft clustering 1335: 1334: 1326:Hard clustering 1325: 1324: 1289: 1288: 1239: 1238: 1228: 1227: 1213: 1212: 1200:: for example, 1194: 1193: 1175: 1174: 1160: 1159: 1151:: for example, 1145: 1144: 1136: 1098: 1095: 1092: 965: 936: 935: 909: 901: 900: 861: 853: 852: 813:Kernel machines 808: 800: 799: 775: 767: 766: 747:Active learning 742: 734: 733: 702: 692: 691: 617:Diffusion model 553: 543: 542: 515: 505: 504: 478: 468: 467: 423:Factor analysis 418: 408: 407: 391: 354: 344: 343: 264: 263: 247: 246: 245: 234: 233: 139: 131: 130: 96:Online learning 61: 49: 28: 23: 22: 18:Data Clustering 15: 12: 11: 5: 11285: 11275: 11274: 11269: 11264: 11247: 11246: 11244: 11243: 11231: 11219: 11205: 11192: 11189: 11188: 11185: 11184: 11181: 11180: 11178: 11177: 11172: 11167: 11162: 11157: 11151: 11149: 11143: 11142: 11140: 11139: 11134: 11129: 11124: 11119: 11114: 11109: 11104: 11099: 11094: 11088: 11086: 11080: 11079: 11077: 11076: 11071: 11066: 11057: 11052: 11047: 11041: 11039: 11033: 11032: 11030: 11029: 11024: 11019: 11010: 11008:Bioinformatics 11004: 11002: 10992: 10991: 10979: 10978: 10975: 10974: 10971: 10970: 10967: 10966: 10964: 10963: 10957: 10955: 10951: 10950: 10948: 10947: 10941: 10939: 10933: 10932: 10930: 10929: 10924: 10919: 10914: 10908: 10906: 10897: 10891: 10890: 10887: 10886: 10884: 10883: 10878: 10873: 10868: 10863: 10857: 10855: 10849: 10848: 10846: 10845: 10840: 10835: 10827: 10822: 10817: 10816: 10815: 10813:partial (PACF) 10804: 10802: 10796: 10795: 10793: 10792: 10787: 10782: 10774: 10769: 10763: 10761: 10760:Specific tests 10757: 10756: 10754: 10753: 10748: 10743: 10738: 10733: 10728: 10723: 10718: 10712: 10710: 10703: 10697: 10696: 10694: 10693: 10692: 10691: 10690: 10689: 10674: 10673: 10672: 10662: 10660:Classification 10657: 10652: 10647: 10642: 10637: 10632: 10626: 10624: 10618: 10617: 10615: 10614: 10609: 10607:McNemar's test 10604: 10599: 10594: 10589: 10583: 10581: 10571: 10570: 10546: 10545: 10542: 10541: 10538: 10537: 10535: 10534: 10529: 10524: 10519: 10513: 10511: 10505: 10504: 10502: 10501: 10485: 10479: 10477: 10471: 10470: 10468: 10467: 10462: 10457: 10452: 10447: 10445:Semiparametric 10442: 10437: 10431: 10429: 10425: 10424: 10422: 10421: 10416: 10411: 10406: 10400: 10398: 10392: 10391: 10389: 10388: 10383: 10378: 10373: 10368: 10362: 10360: 10354: 10353: 10351: 10350: 10345: 10340: 10335: 10329: 10327: 10317: 10316: 10313: 10312: 10307: 10301: 10293: 10292: 10289: 10288: 10285: 10284: 10282: 10281: 10280: 10279: 10269: 10264: 10259: 10258: 10257: 10252: 10241: 10239: 10233: 10232: 10229: 10228: 10226: 10225: 10220: 10219: 10218: 10210: 10202: 10186: 10183:(Mann–Whitney) 10178: 10177: 10176: 10163: 10162: 10161: 10150: 10148: 10142: 10141: 10139: 10138: 10137: 10136: 10131: 10126: 10116: 10111: 10108:(Shapiro–Wilk) 10103: 10098: 10093: 10088: 10083: 10075: 10069: 10067: 10061: 10060: 10058: 10057: 10049: 10040: 10028: 10022: 10020:Specific tests 10016: 10015: 10012: 10011: 10009: 10008: 10003: 9998: 9992: 9990: 9984: 9983: 9981: 9980: 9975: 9974: 9973: 9963: 9962: 9961: 9951: 9945: 9943: 9937: 9936: 9934: 9933: 9932: 9931: 9926: 9916: 9911: 9906: 9901: 9896: 9890: 9888: 9882: 9881: 9879: 9878: 9873: 9872: 9871: 9866: 9865: 9864: 9859: 9844: 9843: 9842: 9837: 9832: 9827: 9816: 9814: 9805: 9799: 9798: 9796: 9795: 9790: 9785: 9784: 9783: 9773: 9768: 9767: 9766: 9756: 9755: 9754: 9749: 9744: 9734: 9729: 9724: 9723: 9722: 9717: 9712: 9696: 9695: 9694: 9689: 9684: 9674: 9673: 9672: 9667: 9657: 9656: 9655: 9645: 9644: 9643: 9633: 9628: 9623: 9617: 9615: 9605: 9604: 9592: 9591: 9588: 9587: 9584: 9583: 9581: 9580: 9575: 9570: 9565: 9559: 9557: 9551: 9550: 9548: 9547: 9542: 9537: 9531: 9529: 9525: 9524: 9522: 9521: 9516: 9511: 9506: 9501: 9496: 9491: 9485: 9483: 9477: 9476: 9474: 9473: 9471:Standard error 9468: 9463: 9458: 9457: 9456: 9451: 9440: 9438: 9432: 9431: 9429: 9428: 9423: 9418: 9413: 9408: 9403: 9401:Optimal design 9398: 9393: 9387: 9385: 9375: 9374: 9362: 9361: 9358: 9357: 9354: 9353: 9351: 9350: 9345: 9340: 9335: 9330: 9325: 9320: 9315: 9310: 9305: 9300: 9295: 9290: 9285: 9280: 9274: 9272: 9266: 9265: 9263: 9262: 9257: 9256: 9255: 9250: 9240: 9235: 9229: 9227: 9221: 9220: 9218: 9217: 9212: 9207: 9201: 9199: 9198:Summary tables 9195: 9194: 9192: 9191: 9185: 9183: 9177: 9176: 9173: 9172: 9170: 9169: 9168: 9167: 9162: 9157: 9147: 9141: 9139: 9133: 9132: 9130: 9129: 9124: 9119: 9114: 9109: 9104: 9099: 9093: 9091: 9085: 9084: 9082: 9081: 9076: 9071: 9070: 9069: 9064: 9059: 9054: 9049: 9044: 9039: 9034: 9032:Contraharmonic 9029: 9024: 9013: 9011: 9002: 8992: 8991: 8979: 8978: 8976: 8975: 8970: 8964: 8961: 8960: 8953: 8952: 8945: 8938: 8930: 8921: 8920: 8918: 8917: 8916: 8915: 8910: 8897: 8896: 8895: 8890: 8876: 8873: 8872: 8870: 8869: 8864: 8859: 8854: 8849: 8844: 8839: 8834: 8829: 8824: 8819: 8814: 8809: 8804: 8799: 8793: 8791: 8787: 8786: 8784: 8783: 8778: 8773: 8768: 8763: 8758: 8753: 8748: 8743: 8737: 8735: 8731: 8730: 8728: 8727: 8725:Ilya Sutskever 8722: 8717: 8712: 8707: 8702: 8697: 8692: 8690:Demis Hassabis 8687: 8682: 8680:Ian Goodfellow 8677: 8672: 8666: 8664: 8660: 8659: 8656: 8655: 8653: 8652: 8647: 8646: 8645: 8635: 8630: 8625: 8620: 8615: 8610: 8605: 8599: 8597: 8593: 8592: 8590: 8589: 8584: 8579: 8574: 8569: 8564: 8559: 8554: 8549: 8544: 8539: 8534: 8529: 8524: 8519: 8514: 8509: 8508: 8507: 8497: 8492: 8487: 8482: 8477: 8471: 8469: 8465: 8464: 8462: 8461: 8456: 8455: 8454: 8449: 8439: 8438: 8437: 8432: 8427: 8417: 8412: 8407: 8402: 8397: 8392: 8387: 8382: 8377: 8371: 8369: 8362: 8358: 8357: 8355: 8354: 8349: 8344: 8339: 8334: 8329: 8324: 8318: 8316: 8312: 8311: 8309: 8308: 8303: 8298: 8293: 8288: 8282: 8280: 8276: 8275: 8273: 8272: 8271: 8270: 8263:Language model 8260: 8255: 8250: 8249: 8248: 8238: 8237: 8236: 8225: 8223: 8219: 8218: 8216: 8215: 8213:Autoregression 8210: 8205: 8204: 8203: 8193: 8191:Regularization 8188: 8187: 8186: 8181: 8176: 8166: 8161: 8156: 8154:Loss functions 8151: 8146: 8141: 8136: 8131: 8130: 8129: 8119: 8114: 8113: 8112: 8101: 8099: 8095: 8094: 8092: 8091: 8089:Inductive bias 8086: 8081: 8076: 8071: 8066: 8061: 8056: 8051: 8043: 8041: 8035: 8034: 8029: 8028: 8021: 8014: 8006: 7998: 7997: 7962: 7927:(1): 105–152. 7904: 7891:(1–3): 17–44. 7871: 7852: 7841:|journal= 7818: 7807: 7788:(3): 709–754. 7769: 7720: 7663: 7620: 7601:(4): 175–181. 7585: 7550:(3): 241–254. 7534: 7519: 7493: 7466: 7417: 7402: 7375: 7340: 7325: 7290: 7243: 7216: 7172: 7145: 7118: 7078: 7071: 7048: 7034:978-0387954332 7033: 7012: 6998:978-0521836579 6997: 6974: 6932: 6871: 6852: 6843:|journal= 6802: 6795: 6769: 6754: 6737:10.1.1.71.5021 6722:; Kröger, P.; 6720:Kriegel, H. P. 6710: 6696:978-1581138597 6695: 6655: 6640: 6600: 6593: 6576:10.1.1.70.7843 6559:Kriegel, H. P. 6549: 6542: 6508:Kriegel, H.-P. 6498: 6477: 6432: 6413:(4): 351–364. 6390: 6377: 6368: 6349:(3): 283–304. 6329: 6314: 6299: 6281: 6274: 6257:10.1.1.64.1161 6235: 6202: 6195: 6169: 6150: 6131:(3): 231–240. 6104: 6085:(2): 129–137. 6069: 6042: 6008: 6001: 5983: 5931: 5923:James A. Davis 5915: 5869: 5858:(4): 476–506. 5842: 5824: 5805:(4): 508–516. 5789: 5758: 5757: 5755: 5752: 5751: 5750: 5745: 5740: 5735: 5730: 5725: 5718: 5715: 5714: 5713: 5708: 5703: 5696: 5693: 5692: 5691: 5686: 5681: 5676: 5671: 5663: 5660: 5659: 5658: 5653: 5648: 5646:HCS clustering 5643: 5638: 5633: 5628: 5623: 5618: 5613: 5608: 5601: 5598: 5596: 5593: 5592: 5591: 5588: 5584: 5583: 5580: 5576: 5575: 5572: 5568: 5567: 5564: 5558: 5557: 5550: 5544: 5543: 5540: 5539:Field robotics 5535: 5532: 5531: 5530: 5527: 5524: 5521: 5516: 5512: 5510:Crime analysis 5507: 5504: 5497: 5496:Social science 5494: 5493: 5492: 5489: 5484: 5477: 5472: 5469: 5464: 5461: 5456: 5452: 5447: 5444: 5439: 5421: 5416: 5412: 5405: 5400: 5399: 5398: 5392: 5389: 5378: 5375: 5364: 5359: 5357:World Wide Web 5354: 5353: 5352: 5344: 5341: 5310: 5303: 5300: 5299: 5298: 5295: 5292: 5288: 5285: 5274: 5267: 5262: 5261: 5260: 5257: 5252: 5249: 5242: 5231:bioinformatics 5220: 5215: 5180: 5175: 5164: 5144: 5141: 5138: 5137: 5096: 5094: 5087: 5081: 5078: 5077: 5076: 5065: 5062: 5061: 5060: 5049: 5039: 5034: 5030: 5023: 5018: 5015: 5012: 5008: 5004: 4998: 4993: 4989: 4982: 4977: 4974: 4971: 4967: 4958: 4953: 4949: 4942: 4937: 4934: 4931: 4927: 4920: 4917: 4895: 4892: 4887: 4883: 4860: 4856: 4835: 4832: 4827: 4823: 4800: 4796: 4775: 4755: 4733: 4729: 4708: 4705: 4702: 4682: 4662: 4653:be the set of 4642: 4626: 4625: 4612: 4609: 4608: 4607: 4603: 4602: 4595: 4578: 4567: 4566: 4536: 4533: 4529: 4506: 4502: 4469: 4449: 4422: 4419: 4395: 4392: 4368: 4365: 4354:true positives 4341: 4338: 4327: 4326: 4325: 4309: 4306: 4303: 4300: 4297: 4292: 4289: 4283: 4277: 4274: 4271: 4268: 4265: 4260: 4257: 4249: 4246: 4243: 4228: 4227: 4219: 4218: 4217: 4216: 4202: 4199: 4196: 4193: 4190: 4187: 4184: 4181: 4178: 4173: 4170: 4167: 4161: 4158: 4155: 4152: 4130: 4127: 4107: 4104: 4092: 4091: 4083: 4082: 4070: 4067: 4056: 4053: 4052: 4051: 4037: 4034: 4031: 4028: 4025: 4022: 4019: 4016: 4011: 4008: 4002: 3995: 3991: 3988: 3985: 3981: 3974: 3970: 3967: 3964: 3960: 3953: 3950: 3947: 3944: 3941: 3938: 3935: 3916: 3915: 3907: 3906: 3894: 3891: 3880: 3868: 3848: 3845: 3842: 3818: 3815: 3810: 3806: 3785: 3782: 3779: 3768: 3767: 3766: 3752: 3749: 3746: 3743: 3738: 3734: 3728: 3725: 3722: 3719: 3716: 3713: 3710: 3705: 3701: 3697: 3691: 3686: 3682: 3655: 3631: 3620: 3619: 3618: 3604: 3601: 3598: 3595: 3592: 3587: 3584: 3578: 3575: 3565: 3551: 3548: 3545: 3542: 3539: 3534: 3531: 3525: 3522: 3488: 3485: 3482: 3462: 3461: 3434: 3433: 3418: 3413: 3410: 3405: 3399: 3396: 3393: 3390: 3387: 3384: 3381: 3378: 3375: 3372: 3369: 3366: 3346: 3343: 3323: 3320: 3292: 3289: 3265: 3262: 3251:true negatives 3238: 3235: 3215: 3212: 3201: 3200: 3199: 3185: 3182: 3179: 3176: 3173: 3170: 3167: 3164: 3161: 3158: 3155: 3150: 3147: 3144: 3141: 3138: 3132: 3129: 3126: 3112: 3111: 3103: 3102: 3098: 3097: 3096: 3083: 3079: 3076: 3073: 3069: 3062: 3059: 3056: 3052: 3046: 3043: 3040: 3036: 3030: 3027: 3012: 3011: 2999: 2979: 2959: 2934:true positives 2908: 2905: 2904: 2903: 2894: 2893: 2885: 2884: 2821: 2820: 2819: 2808: 2801: 2798: 2795: 2790: 2786: 2780: 2777: 2774: 2771: 2768: 2764: 2758: 2755: 2752: 2749: 2746: 2743: 2738: 2735: 2732: 2729: 2726: 2723: 2720: 2716: 2709: 2706: 2691: 2690: 2682: 2681: 2663: 2659: 2636: 2632: 2611: 2606: 2602: 2598: 2593: 2589: 2585: 2582: 2560: 2556: 2535: 2513: 2509: 2488: 2462: 2458: 2442: 2441: 2440: 2428: 2422: 2417: 2413: 2409: 2404: 2400: 2396: 2393: 2386: 2382: 2378: 2373: 2369: 2362: 2356: 2353: 2350: 2346: 2340: 2335: 2332: 2329: 2325: 2319: 2316: 2311: 2308: 2305: 2287: 2286: 2255: 2252: 2219: 2216: 2161:that focus on 2121: 2118: 2117: 2116: 2113: 2110: 2109: 2108: 2105: 2102: 2096: 2093: 2090: 2073: 2070: 2069: 2068: 2062: 2055: 2053: 2047: 2040: 2038: 2032: 2025: 2023: 1977: 1949: 1921: 1918: 1917: 1916: 1913: 1906: 1904: 1897: 1890: 1888: 1833: 1830: 1814: 1813: 1807: 1800: 1798: 1792: 1785: 1783: 1668:Main article: 1665: 1662: 1661: 1660: 1657: 1650: 1648: 1645: 1638: 1636: 1620: 1615: 1611: 1607: 1602: 1576: 1571: 1568: 1565: 1561: 1557: 1552: 1530: 1525: 1521: 1517: 1512: 1450:Main article: 1447: 1444: 1424: 1421: 1420: 1419: 1407: 1397: 1379: 1366: 1352: 1351: 1331: 1316: 1315: 1300:neural network 1285: 1278:balance theory 1259: 1235: 1224: 1214:Subspace model 1209: 1190: 1171: 1161:Centroid model 1156: 1135: 1132: 1071:classification 1011:bioinformatics 1003:image analysis 967: 966: 964: 963: 956: 949: 941: 938: 937: 934: 933: 928: 927: 926: 916: 910: 907: 906: 903: 902: 899: 898: 893: 888: 883: 878: 873: 868: 862: 859: 858: 855: 854: 851: 850: 845: 840: 835: 833:Occam learning 830: 825: 820: 815: 809: 806: 805: 802: 801: 798: 797: 792: 790:Learning curve 787: 782: 776: 773: 772: 769: 768: 765: 764: 759: 754: 749: 743: 740: 739: 736: 735: 732: 731: 730: 729: 719: 714: 709: 703: 698: 697: 694: 693: 690: 689: 683: 678: 673: 668: 667: 666: 656: 651: 650: 649: 644: 639: 634: 624: 619: 614: 609: 608: 607: 597: 596: 595: 590: 585: 580: 570: 565: 560: 554: 549: 548: 545: 544: 541: 540: 535: 530: 522: 516: 511: 510: 507: 506: 503: 502: 501: 500: 495: 490: 479: 474: 473: 470: 469: 466: 465: 460: 455: 450: 445: 440: 435: 430: 425: 419: 414: 413: 410: 409: 406: 405: 400: 395: 389: 384: 379: 371: 366: 361: 355: 350: 349: 346: 345: 342: 341: 336: 331: 326: 321: 316: 311: 306: 298: 297: 296: 291: 286: 276: 274:Decision trees 271: 265: 251:classification 241: 240: 239: 236: 235: 232: 231: 226: 221: 216: 211: 206: 201: 196: 191: 186: 181: 176: 171: 166: 161: 156: 151: 146: 144:Classification 140: 137: 136: 133: 132: 129: 128: 123: 118: 113: 108: 103: 101:Batch learning 98: 93: 88: 83: 78: 73: 68: 62: 59: 58: 55: 54: 43: 42: 26: 9: 6: 4: 3: 2: 11284: 11273: 11272:Geostatistics 11270: 11268: 11265: 11263: 11260: 11259: 11257: 11242: 11241: 11232: 11230: 11229: 11220: 11218: 11217: 11212: 11206: 11204: 11203: 11194: 11193: 11190: 11176: 11173: 11171: 11170:Geostatistics 11168: 11166: 11163: 11161: 11158: 11156: 11153: 11152: 11150: 11148: 11144: 11138: 11137:Psychometrics 11135: 11133: 11130: 11128: 11125: 11123: 11120: 11118: 11115: 11113: 11110: 11108: 11105: 11103: 11100: 11098: 11095: 11093: 11090: 11089: 11087: 11085: 11081: 11075: 11072: 11070: 11067: 11065: 11061: 11058: 11056: 11053: 11051: 11048: 11046: 11043: 11042: 11040: 11038: 11034: 11028: 11025: 11023: 11020: 11018: 11014: 11011: 11009: 11006: 11005: 11003: 11001: 11000:Biostatistics 10997: 10993: 10989: 10984: 10980: 10962: 10961:Log-rank test 10959: 10958: 10956: 10952: 10946: 10943: 10942: 10940: 10938: 10934: 10928: 10925: 10923: 10920: 10918: 10915: 10913: 10910: 10909: 10907: 10905: 10901: 10898: 10896: 10892: 10882: 10879: 10877: 10874: 10872: 10869: 10867: 10864: 10862: 10859: 10858: 10856: 10854: 10850: 10844: 10841: 10839: 10836: 10834: 10832:(Box–Jenkins) 10828: 10826: 10823: 10821: 10818: 10814: 10811: 10810: 10809: 10806: 10805: 10803: 10801: 10797: 10791: 10788: 10786: 10785:Durbin–Watson 10783: 10781: 10775: 10773: 10770: 10768: 10767:Dickey–Fuller 10765: 10764: 10762: 10758: 10752: 10749: 10747: 10744: 10742: 10741:Cointegration 10739: 10737: 10734: 10732: 10729: 10727: 10724: 10722: 10719: 10717: 10716:Decomposition 10714: 10713: 10711: 10707: 10704: 10702: 10698: 10688: 10685: 10684: 10683: 10680: 10679: 10678: 10675: 10671: 10668: 10667: 10666: 10663: 10661: 10658: 10656: 10653: 10651: 10648: 10646: 10643: 10641: 10638: 10636: 10633: 10631: 10628: 10627: 10625: 10623: 10619: 10613: 10610: 10608: 10605: 10603: 10600: 10598: 10595: 10593: 10590: 10588: 10587:Cohen's kappa 10585: 10584: 10582: 10580: 10576: 10572: 10568: 10564: 10560: 10556: 10551: 10547: 10533: 10530: 10528: 10525: 10523: 10520: 10518: 10515: 10514: 10512: 10510: 10506: 10500: 10496: 10492: 10486: 10484: 10481: 10480: 10478: 10476: 10472: 10466: 10463: 10461: 10458: 10456: 10453: 10451: 10448: 10446: 10443: 10441: 10440:Nonparametric 10438: 10436: 10433: 10432: 10430: 10426: 10420: 10417: 10415: 10412: 10410: 10407: 10405: 10402: 10401: 10399: 10397: 10393: 10387: 10384: 10382: 10379: 10377: 10374: 10372: 10369: 10367: 10364: 10363: 10361: 10359: 10355: 10349: 10346: 10344: 10341: 10339: 10336: 10334: 10331: 10330: 10328: 10326: 10322: 10318: 10311: 10308: 10306: 10303: 10302: 10298: 10294: 10278: 10275: 10274: 10273: 10270: 10268: 10265: 10263: 10260: 10256: 10253: 10251: 10248: 10247: 10246: 10243: 10242: 10240: 10238: 10234: 10224: 10221: 10217: 10211: 10209: 10203: 10201: 10195: 10194: 10193: 10190: 10189:Nonparametric 10187: 10185: 10179: 10175: 10172: 10171: 10170: 10164: 10160: 10159:Sample median 10157: 10156: 10155: 10152: 10151: 10149: 10147: 10143: 10135: 10132: 10130: 10127: 10125: 10122: 10121: 10120: 10117: 10115: 10112: 10110: 10104: 10102: 10099: 10097: 10094: 10092: 10089: 10087: 10084: 10082: 10080: 10076: 10074: 10071: 10070: 10068: 10066: 10062: 10056: 10054: 10050: 10048: 10046: 10041: 10039: 10034: 10030: 10029: 10026: 10023: 10021: 10017: 10007: 10004: 10002: 9999: 9997: 9994: 9993: 9991: 9989: 9985: 9979: 9976: 9972: 9969: 9968: 9967: 9964: 9960: 9957: 9956: 9955: 9952: 9950: 9947: 9946: 9944: 9942: 9938: 9930: 9927: 9925: 9922: 9921: 9920: 9917: 9915: 9912: 9910: 9907: 9905: 9902: 9900: 9897: 9895: 9892: 9891: 9889: 9887: 9883: 9877: 9874: 9870: 9867: 9863: 9860: 9858: 9855: 9854: 9853: 9850: 9849: 9848: 9845: 9841: 9838: 9836: 9833: 9831: 9828: 9826: 9823: 9822: 9821: 9818: 9817: 9815: 9813: 9809: 9806: 9804: 9800: 9794: 9791: 9789: 9786: 9782: 9779: 9778: 9777: 9774: 9772: 9769: 9765: 9764:loss function 9762: 9761: 9760: 9757: 9753: 9750: 9748: 9745: 9743: 9740: 9739: 9738: 9735: 9733: 9730: 9728: 9725: 9721: 9718: 9716: 9713: 9711: 9705: 9702: 9701: 9700: 9697: 9693: 9690: 9688: 9685: 9683: 9680: 9679: 9678: 9675: 9671: 9668: 9666: 9663: 9662: 9661: 9658: 9654: 9651: 9650: 9649: 9646: 9642: 9639: 9638: 9637: 9634: 9632: 9629: 9627: 9624: 9622: 9619: 9618: 9616: 9614: 9610: 9606: 9602: 9597: 9593: 9579: 9576: 9574: 9571: 9569: 9566: 9564: 9561: 9560: 9558: 9556: 9552: 9546: 9543: 9541: 9538: 9536: 9533: 9532: 9530: 9526: 9520: 9517: 9515: 9512: 9510: 9507: 9505: 9502: 9500: 9497: 9495: 9492: 9490: 9487: 9486: 9484: 9482: 9478: 9472: 9469: 9467: 9466:Questionnaire 9464: 9462: 9459: 9455: 9452: 9450: 9447: 9446: 9445: 9442: 9441: 9439: 9437: 9433: 9427: 9424: 9422: 9419: 9417: 9414: 9412: 9409: 9407: 9404: 9402: 9399: 9397: 9394: 9392: 9389: 9388: 9386: 9384: 9380: 9376: 9372: 9367: 9363: 9349: 9346: 9344: 9341: 9339: 9336: 9334: 9331: 9329: 9326: 9324: 9321: 9319: 9316: 9314: 9311: 9309: 9306: 9304: 9301: 9299: 9296: 9294: 9293:Control chart 9291: 9289: 9286: 9284: 9281: 9279: 9276: 9275: 9273: 9271: 9267: 9261: 9258: 9254: 9251: 9249: 9246: 9245: 9244: 9241: 9239: 9236: 9234: 9231: 9230: 9228: 9226: 9222: 9216: 9213: 9211: 9208: 9206: 9203: 9202: 9200: 9196: 9190: 9187: 9186: 9184: 9182: 9178: 9166: 9163: 9161: 9158: 9156: 9153: 9152: 9151: 9148: 9146: 9143: 9142: 9140: 9138: 9134: 9128: 9125: 9123: 9120: 9118: 9115: 9113: 9110: 9108: 9105: 9103: 9100: 9098: 9095: 9094: 9092: 9090: 9086: 9080: 9077: 9075: 9072: 9068: 9065: 9063: 9060: 9058: 9055: 9053: 9050: 9048: 9045: 9043: 9040: 9038: 9035: 9033: 9030: 9028: 9025: 9023: 9020: 9019: 9018: 9015: 9014: 9012: 9010: 9006: 9003: 9001: 8997: 8993: 8989: 8984: 8980: 8974: 8971: 8969: 8966: 8965: 8962: 8958: 8951: 8946: 8944: 8939: 8937: 8932: 8931: 8928: 8914: 8911: 8909: 8906: 8905: 8898: 8894: 8891: 8889: 8886: 8885: 8882: 8878: 8877: 8874: 8868: 8865: 8863: 8860: 8858: 8855: 8853: 8850: 8848: 8845: 8843: 8840: 8838: 8835: 8833: 8830: 8828: 8825: 8823: 8820: 8818: 8815: 8813: 8810: 8808: 8805: 8803: 8800: 8798: 8795: 8794: 8792: 8790:Architectures 8788: 8782: 8779: 8777: 8774: 8772: 8769: 8767: 8764: 8762: 8759: 8757: 8754: 8752: 8749: 8747: 8744: 8742: 8739: 8738: 8736: 8734:Organizations 8732: 8726: 8723: 8721: 8718: 8716: 8713: 8711: 8708: 8706: 8703: 8701: 8698: 8696: 8693: 8691: 8688: 8686: 8683: 8681: 8678: 8676: 8673: 8671: 8670:Yoshua Bengio 8668: 8667: 8665: 8661: 8651: 8650:Robot control 8648: 8644: 8641: 8640: 8639: 8636: 8634: 8631: 8629: 8626: 8624: 8621: 8619: 8616: 8614: 8611: 8609: 8606: 8604: 8601: 8600: 8598: 8594: 8588: 8585: 8583: 8580: 8578: 8575: 8573: 8570: 8568: 8567:Chinchilla AI 8565: 8563: 8560: 8558: 8555: 8553: 8550: 8548: 8545: 8543: 8540: 8538: 8535: 8533: 8530: 8528: 8525: 8523: 8520: 8518: 8515: 8513: 8510: 8506: 8503: 8502: 8501: 8498: 8496: 8493: 8491: 8488: 8486: 8483: 8481: 8478: 8476: 8473: 8472: 8470: 8466: 8460: 8457: 8453: 8450: 8448: 8445: 8444: 8443: 8440: 8436: 8433: 8431: 8428: 8426: 8423: 8422: 8421: 8418: 8416: 8413: 8411: 8408: 8406: 8403: 8401: 8398: 8396: 8393: 8391: 8388: 8386: 8383: 8381: 8378: 8376: 8373: 8372: 8370: 8366: 8363: 8359: 8353: 8350: 8348: 8345: 8343: 8340: 8338: 8335: 8333: 8330: 8328: 8325: 8323: 8320: 8319: 8317: 8313: 8307: 8304: 8302: 8299: 8297: 8294: 8292: 8289: 8287: 8284: 8283: 8281: 8277: 8269: 8266: 8265: 8264: 8261: 8259: 8256: 8254: 8251: 8247: 8246:Deep learning 8244: 8243: 8242: 8239: 8235: 8232: 8231: 8230: 8227: 8226: 8224: 8220: 8214: 8211: 8209: 8206: 8202: 8199: 8198: 8197: 8194: 8192: 8189: 8185: 8182: 8180: 8177: 8175: 8172: 8171: 8170: 8167: 8165: 8162: 8160: 8157: 8155: 8152: 8150: 8147: 8145: 8142: 8140: 8137: 8135: 8134:Hallucination 8132: 8128: 8125: 8124: 8123: 8120: 8118: 8115: 8111: 8108: 8107: 8106: 8103: 8102: 8100: 8096: 8090: 8087: 8085: 8082: 8080: 8077: 8075: 8072: 8070: 8067: 8065: 8062: 8060: 8057: 8055: 8052: 8050: 8049: 8045: 8044: 8042: 8040: 8036: 8027: 8022: 8020: 8015: 8013: 8008: 8007: 8004: 7993: 7989: 7985: 7981: 7977: 7973: 7966: 7958: 7954: 7950: 7946: 7942: 7938: 7934: 7930: 7926: 7922: 7915: 7908: 7899: 7894: 7890: 7886: 7882: 7875: 7867: 7863: 7856: 7850: 7846: 7833: 7822: 7816: 7811: 7803: 7799: 7795: 7791: 7787: 7783: 7776: 7774: 7765: 7761: 7756: 7751: 7747: 7743: 7739: 7735: 7731: 7724: 7716: 7712: 7707: 7702: 7698: 7694: 7690: 7686: 7682: 7678: 7674: 7667: 7659: 7655: 7651: 7647: 7643: 7639: 7635: 7631: 7624: 7616: 7612: 7608: 7604: 7600: 7596: 7589: 7581: 7577: 7573: 7569: 7565: 7561: 7557: 7553: 7549: 7545: 7544:Psychometrika 7538: 7530: 7526: 7522: 7516: 7512: 7508: 7504: 7497: 7489: 7485: 7481: 7477: 7470: 7462: 7458: 7453: 7448: 7444: 7440: 7436: 7432: 7428: 7421: 7413: 7406: 7398: 7394: 7390: 7386: 7379: 7371: 7367: 7363: 7359: 7355: 7351: 7344: 7336: 7329: 7321: 7317: 7313: 7309: 7305: 7301: 7294: 7286: 7282: 7278: 7274: 7269: 7264: 7260: 7256: 7255: 7247: 7239: 7235: 7231: 7227: 7220: 7212: 7209: 7205: 7201: 7194: 7190: 7189:Zimek, Arthur 7186: 7179: 7177: 7168: 7164: 7160: 7156: 7149: 7141: 7137: 7133: 7129: 7122: 7114: 7108: 7100: 7093: 7092: 7085: 7083: 7074: 7068: 7064: 7057: 7055: 7053: 7044: 7040: 7036: 7030: 7026: 7019: 7017: 7008: 7004: 7000: 6994: 6990: 6983: 6981: 6979: 6970: 6966: 6962: 6958: 6954: 6950: 6943: 6941: 6939: 6937: 6928: 6924: 6920: 6916: 6912: 6908: 6903: 6898: 6894: 6890: 6886: 6882: 6875: 6867: 6863: 6856: 6848: 6835: 6827: 6823: 6818: 6817:q-bio/0311039 6813: 6806: 6798: 6792: 6788: 6784: 6780: 6773: 6765: 6761: 6757: 6751: 6747: 6743: 6738: 6733: 6730:. p. 7. 6729: 6725: 6721: 6714: 6706: 6702: 6698: 6692: 6688: 6684: 6679: 6678:10.1.1.5.1279 6674: 6670: 6666: 6659: 6651: 6647: 6643: 6637: 6633: 6629: 6624: 6619: 6615: 6611: 6604: 6596: 6590: 6586: 6582: 6577: 6572: 6568: 6564: 6560: 6553: 6545: 6539: 6535: 6531: 6526: 6521: 6517: 6513: 6509: 6502: 6495: 6491: 6487: 6481: 6473: 6469: 6465: 6461: 6456: 6451: 6447: 6443: 6436: 6428: 6424: 6420: 6416: 6412: 6408: 6404: 6403:Zimek, Arthur 6400: 6394: 6387: 6381: 6372: 6364: 6360: 6356: 6352: 6348: 6344: 6340: 6333: 6325: 6318: 6310: 6306: 6302: 6296: 6292: 6285: 6277: 6271: 6267: 6263: 6258: 6253: 6249: 6242: 6240: 6230: 6225: 6221: 6217: 6213: 6206: 6198: 6196:1-57735-004-9 6192: 6188: 6184: 6180: 6173: 6166: 6162: 6159: 6154: 6146: 6142: 6138: 6134: 6130: 6126: 6122: 6118: 6117:Zimek, Arthur 6114: 6108: 6100: 6096: 6092: 6088: 6084: 6080: 6073: 6065: 6061: 6057: 6053: 6046: 6038: 6034: 6030: 6026: 6019: 6012: 6004: 6002:9780470749913 5998: 5994: 5987: 5979: 5975: 5970: 5965: 5960: 5955: 5951: 5947: 5943: 5935: 5928: 5924: 5919: 5911: 5907: 5903: 5899: 5895: 5891: 5884: 5882: 5880: 5878: 5876: 5874: 5865: 5861: 5857: 5853: 5846: 5838: 5834: 5828: 5820: 5816: 5812: 5808: 5804: 5800: 5793: 5779:on 2020-12-06 5778: 5774: 5770: 5763: 5759: 5749: 5746: 5744: 5741: 5739: 5736: 5734: 5731: 5729: 5726: 5724: 5721: 5720: 5712: 5709: 5707: 5704: 5702: 5699: 5698: 5690: 5687: 5685: 5682: 5680: 5677: 5675: 5672: 5669: 5666: 5665: 5657: 5654: 5652: 5649: 5647: 5644: 5642: 5639: 5637: 5634: 5632: 5629: 5627: 5624: 5622: 5619: 5617: 5614: 5612: 5609: 5607: 5604: 5603: 5589: 5586: 5585: 5581: 5578: 5577: 5573: 5570: 5569: 5565: 5563: 5560: 5559: 5555: 5551: 5549: 5546: 5545: 5541: 5538: 5537: 5528: 5525: 5522: 5520: 5517: 5513: 5511: 5508: 5505: 5503: 5500: 5499: 5490: 5488: 5485: 5482: 5478: 5476: 5473: 5470: 5468: 5465: 5462: 5460: 5457: 5453: 5451: 5448: 5445: 5443: 5440: 5437: 5433: 5429: 5426: 5422: 5420: 5417: 5413: 5411: 5408: 5407: 5404: 5396: 5393: 5390: 5387: 5383: 5379: 5376: 5373: 5369: 5365: 5362: 5361: 5358: 5350: 5345: 5342: 5339: 5335: 5331: 5327: 5323: 5319: 5315: 5311: 5309: 5306: 5305: 5296: 5293: 5289: 5286: 5283: 5279: 5275: 5273: 5270: 5269: 5266: 5258: 5256: 5253: 5250: 5247: 5243: 5240: 5236: 5232: 5228: 5227:gene families 5224: 5221: 5219: 5216: 5213: 5209: 5205: 5201: 5197: 5193: 5189: 5185: 5181: 5179: 5176: 5173: 5169: 5165: 5163: 5160: 5156: 5153: 5152: 5150: 5134: 5131: 5123: 5120:November 2016 5113: 5109: 5103: 5102: 5097:This section 5095: 5091: 5086: 5085: 5074: 5073:multimodality 5070: 5066: 5063: 5047: 5037: 5032: 5028: 5021: 5016: 5013: 5010: 5006: 5002: 4996: 4991: 4987: 4980: 4975: 4972: 4969: 4965: 4956: 4951: 4947: 4940: 4935: 4932: 4929: 4925: 4918: 4915: 4908: 4907: 4893: 4890: 4885: 4881: 4858: 4854: 4833: 4830: 4825: 4821: 4798: 4794: 4773: 4753: 4731: 4727: 4706: 4703: 4700: 4680: 4660: 4640: 4632: 4628: 4627: 4624: 4623: 4619: 4618: 4617: 4605: 4604: 4601: 4600: 4596: 4593: 4589: 4585: 4584: 4579: 4576: 4572: 4569: 4568: 4564: 4560: 4556: 4552: 4534: 4531: 4527: 4504: 4500: 4491: 4487: 4483: 4467: 4447: 4440: 4436: 4420: 4417: 4409: 4393: 4390: 4382: 4366: 4363: 4355: 4339: 4336: 4328: 4307: 4304: 4301: 4298: 4295: 4290: 4287: 4281: 4275: 4272: 4269: 4266: 4263: 4258: 4255: 4247: 4244: 4241: 4234: 4233: 4230: 4229: 4226: 4225: 4221: 4220: 4200: 4197: 4194: 4191: 4188: 4185: 4182: 4179: 4176: 4171: 4168: 4165: 4159: 4156: 4153: 4150: 4143: 4142: 4128: 4125: 4105: 4102: 4094: 4093: 4090: 4089: 4085: 4084: 4068: 4065: 4057: 4054: 4035: 4032: 4029: 4026: 4023: 4020: 4017: 4014: 4009: 4006: 4000: 3989: 3986: 3983: 3968: 3965: 3962: 3951: 3945: 3942: 3939: 3933: 3926: 3925: 3922: 3921:Jaccard index 3918: 3917: 3914: 3913: 3912:Jaccard index 3909: 3908: 3892: 3889: 3881: 3866: 3846: 3843: 3840: 3832: 3816: 3813: 3808: 3804: 3783: 3780: 3777: 3769: 3750: 3747: 3744: 3741: 3736: 3732: 3726: 3723: 3720: 3717: 3711: 3708: 3703: 3699: 3689: 3684: 3680: 3672: 3671: 3669: 3653: 3645: 3629: 3621: 3602: 3599: 3596: 3593: 3590: 3585: 3582: 3576: 3573: 3566: 3549: 3546: 3543: 3540: 3537: 3532: 3529: 3523: 3520: 3513: 3512: 3510: 3509: 3504: 3503: 3486: 3483: 3480: 3472: 3469:by weighting 3468: 3464: 3463: 3460: 3459: 3455: 3454: 3453: 3451: 3447: 3443: 3439: 3411: 3408: 3397: 3394: 3391: 3388: 3385: 3382: 3379: 3376: 3373: 3370: 3367: 3364: 3344: 3341: 3321: 3318: 3310: 3306: 3290: 3287: 3279: 3263: 3260: 3252: 3236: 3233: 3213: 3210: 3202: 3183: 3180: 3177: 3174: 3171: 3168: 3165: 3162: 3159: 3156: 3153: 3148: 3145: 3142: 3139: 3136: 3130: 3127: 3124: 3117: 3116: 3114: 3113: 3110: 3109: 3105: 3104: 3099: 3077: 3074: 3071: 3060: 3057: 3054: 3044: 3041: 3038: 3034: 3028: 3025: 3016: 3015: 3014: 3013: 2997: 2977: 2957: 2949: 2946: 2945: 2944: 2941: 2939: 2938:pair counting 2935: 2930: 2928: 2924: 2920: 2915: 2914:gold standard 2901: 2896: 2895: 2892: 2891: 2887: 2886: 2882: 2878: 2874: 2870: 2866: 2862: 2858: 2854: 2850: 2846: 2842: 2838: 2834: 2830: 2826: 2822: 2806: 2796: 2784: 2778: 2775: 2772: 2769: 2766: 2753: 2750: 2747: 2741: 2736: 2733: 2730: 2727: 2724: 2721: 2718: 2707: 2704: 2697: 2696: 2693: 2692: 2689: 2688: 2684: 2683: 2679: 2661: 2657: 2634: 2630: 2604: 2600: 2596: 2591: 2587: 2580: 2558: 2554: 2533: 2511: 2507: 2486: 2478: 2460: 2456: 2447: 2443: 2426: 2415: 2411: 2407: 2402: 2398: 2391: 2384: 2380: 2376: 2371: 2367: 2360: 2354: 2351: 2348: 2338: 2333: 2330: 2327: 2323: 2317: 2314: 2309: 2306: 2303: 2296: 2295: 2293: 2289: 2288: 2285: 2284: 2280: 2279: 2278: 2274: 2272: 2266: 2261: 2251: 2247: 2243: 2239: 2237: 2233: 2229: 2225: 2215: 2213: 2209: 2205: 2201: 2200: 2195: 2190: 2187: 2183: 2178: 2176: 2172: 2168: 2164: 2160: 2156: 2152: 2147: 2145: 2141: 2137: 2133: 2132: 2127: 2114: 2111: 2106: 2103: 2100: 2099: 2097: 2094: 2091: 2088: 2087: 2086: 2084: 2079: 2065: 2059: 2054: 2050: 2044: 2039: 2036: 2029: 2024: 2021: 2020: 2019: 2017: 2013: 2009: 2007: 2006:EM clustering 2002: 1998: 1993: 1991: 1975: 1967: 1963: 1947: 1939: 1935: 1934:deterministic 1931: 1926: 1910: 1905: 1894: 1889: 1886: 1885: 1884: 1881: 1876: 1874: 1873:local optimum 1870: 1866: 1861: 1859: 1855: 1850: 1845: 1843: 1839: 1829: 1827: 1823: 1819: 1810: 1804: 1799: 1795: 1789: 1784: 1781: 1778: 1777: 1776: 1774: 1770: 1766: 1761: 1759: 1755: 1751: 1746: 1744: 1743:fuzzy c-means 1740: 1738: 1733: 1731: 1726: 1722: 1720: 1715: 1711: 1710:local optimum 1707: 1703: 1699: 1695: 1690: 1688: 1684: 1682: 1677: 1671: 1654: 1649: 1642: 1637: 1634: 1633: 1632: 1613: 1609: 1590: 1569: 1566: 1563: 1559: 1523: 1519: 1500: 1494: 1492: 1488: 1484: 1480: 1476: 1471: 1469: 1465: 1461: 1460: 1453: 1443: 1439: 1437: 1430: 1417: 1414: 1408: 1405: 1398: 1395: 1391: 1387: 1380: 1378: 1374: 1367: 1364: 1357: 1356: 1355: 1349: 1346: 1339: 1332: 1329: 1322: 1321: 1320: 1313: 1309: 1305: 1301: 1298: 1294: 1286: 1283: 1279: 1275: 1271: 1267: 1263: 1260: 1257: 1252: 1248: 1244: 1236: 1233: 1225: 1222: 1218: 1210: 1207: 1203: 1199: 1195:Density model 1191: 1188: 1184: 1180: 1172: 1169: 1165: 1157: 1154: 1150: 1142: 1141: 1140: 1131: 1129: 1125: 1121: 1117: 1112: 1110: 1109: 1104: 1087: 1083: 1079: 1078: 1073: 1072: 1066: 1061: 1059: 1055: 1051: 1047: 1043: 1039: 1035: 1031: 1026: 1024: 1020: 1016: 1012: 1008: 1004: 1000: 996: 995:data analysis 993: 989: 985: 981: 977: 973: 962: 957: 955: 950: 948: 943: 942: 940: 939: 932: 929: 925: 922: 921: 920: 917: 915: 912: 911: 905: 904: 897: 894: 892: 889: 887: 884: 882: 879: 877: 874: 872: 869: 867: 864: 863: 857: 856: 849: 846: 844: 841: 839: 836: 834: 831: 829: 826: 824: 821: 819: 816: 814: 811: 810: 804: 803: 796: 793: 791: 788: 786: 783: 781: 778: 777: 771: 770: 763: 760: 758: 755: 753: 752:Crowdsourcing 750: 748: 745: 744: 738: 737: 728: 725: 724: 723: 720: 718: 715: 713: 710: 708: 705: 704: 701: 696: 695: 687: 684: 682: 681:Memtransistor 679: 677: 674: 672: 669: 665: 662: 661: 660: 657: 655: 652: 648: 645: 643: 640: 638: 635: 633: 630: 629: 628: 625: 623: 620: 618: 615: 613: 610: 606: 603: 602: 601: 598: 594: 591: 589: 586: 584: 581: 579: 576: 575: 574: 571: 569: 566: 564: 563:Deep learning 561: 559: 556: 555: 552: 547: 546: 539: 536: 534: 531: 529: 527: 523: 521: 518: 517: 514: 509: 508: 499: 498:Hidden Markov 496: 494: 491: 489: 486: 485: 484: 481: 480: 477: 472: 471: 464: 461: 459: 456: 454: 451: 449: 446: 444: 441: 439: 436: 434: 431: 429: 426: 424: 421: 420: 417: 412: 411: 404: 401: 399: 396: 394: 390: 388: 385: 383: 380: 378: 376: 372: 370: 367: 365: 362: 360: 357: 356: 353: 348: 347: 340: 337: 335: 332: 330: 327: 325: 322: 320: 317: 315: 312: 310: 307: 305: 303: 299: 295: 294:Random forest 292: 290: 287: 285: 282: 281: 280: 277: 275: 272: 270: 267: 266: 259: 258: 253: 252: 244: 238: 237: 230: 227: 225: 222: 220: 217: 215: 212: 210: 207: 205: 202: 200: 197: 195: 192: 190: 187: 185: 182: 180: 179:Data cleaning 177: 175: 172: 170: 167: 165: 162: 160: 157: 155: 152: 150: 147: 145: 142: 141: 135: 134: 127: 124: 122: 119: 117: 114: 112: 109: 107: 104: 102: 99: 97: 94: 92: 91:Meta-learning 89: 87: 84: 82: 79: 77: 74: 72: 69: 67: 64: 63: 57: 56: 53: 48: 45: 44: 40: 39: 32: 19: 11238: 11226: 11207: 11200: 11112:Econometrics 11062: / 11045:Chemometrics 11022:Epidemiology 11015: / 10988:Applications 10830:ARIMA model 10777:Q-statistic 10726:Stationarity 10654: 10622:Multivariate 10565: / 10561: / 10559:Multivariate 10557: / 10497: / 10493: / 10267:Bayes factor 10166:Signed rank 10078: 10052: 10044: 10032: 9727:Completeness 9563:Cohort study 9461:Opinion poll 9396:Missing data 9383:Study design 9338:Scatter plot 9260:Scatter plot 9253:Spearman's ρ 9215:Grouped data 8756:Hugging Face 8720:David Silver 8368:Audio–visual 8222:Applications 8201:Augmentation 8116: 8046: 7978:(6): 56–62. 7975: 7971: 7965: 7924: 7920: 7907: 7888: 7884: 7874: 7868:: 1571–1576. 7865: 7861: 7855: 7832:cite journal 7821: 7810: 7785: 7781: 7737: 7733: 7723: 7680: 7676: 7666: 7633: 7629: 7623: 7598: 7594: 7588: 7547: 7543: 7537: 7502: 7496: 7479: 7475: 7469: 7452:11441/132081 7434: 7430: 7420: 7411: 7405: 7388: 7384: 7378: 7353: 7349: 7343: 7334: 7328: 7303: 7299: 7293: 7258: 7252: 7246: 7229: 7219: 7203: 7200:Dy, Jennifer 7158: 7154: 7148: 7131: 7127: 7121: 7090: 7062: 7027:. Springer. 7024: 6988: 6952: 6948: 6884: 6880: 6874: 6865: 6855: 6834:cite journal 6805: 6778: 6772: 6727: 6713: 6668: 6658: 6613: 6603: 6566: 6552: 6515: 6501: 6493: 6489: 6480: 6445: 6441: 6435: 6410: 6406: 6393: 6380: 6371: 6346: 6342: 6338: 6332: 6323: 6317: 6290: 6284: 6247: 6215: 6205: 6182: 6172: 6153: 6128: 6124: 6107: 6082: 6078: 6072: 6055: 6051: 6045: 6028: 6024: 6011: 5992: 5986: 5949: 5945: 5934: 5918: 5896:(1): 65–75. 5893: 5889: 5855: 5851: 5845: 5836: 5827: 5802: 5798: 5792: 5781:. Retrieved 5777:the original 5772: 5762: 5587:Geochemistry 5515:effectively. 5415:maintenance. 5126: 5117: 5106:Please help 5101:verification 5098: 5080:Applications 5068: 4620: 4614: 4597: 4581: 4570: 4551:Informedness 4222: 4086: 3910: 3506: 3500: 3456: 3435: 3308: 3106: 2947: 2942: 2937: 2931: 2910: 2899: 2888: 2880: 2876: 2872: 2864: 2860: 2856: 2852: 2848: 2844: 2840: 2836: 2832: 2828: 2824: 2685: 2546:to centroid 2445: 2281: 2275: 2270: 2267: 2263: 2248: 2244: 2240: 2235: 2231: 2227: 2223: 2221: 2197: 2191: 2179: 2148: 2129: 2125: 2123: 2075: 2010: 1994: 1927: 1923: 1877: 1862: 1846: 1835: 1821: 1817: 1815: 1808: 1793: 1779: 1762: 1757: 1749: 1747: 1736: 1729: 1723:), choosing 1718: 1713: 1704:" (although 1701: 1691: 1686: 1680: 1675: 1673: 1495: 1472: 1457: 1455: 1440: 1432: 1409: 1399: 1393: 1389: 1381: 1368: 1358: 1353: 1341: 1333: 1323: 1317: 1297:unsupervised 1290:Neural model 1287: 1270:signed graph 1261: 1237: 1226: 1221:biclustering 1211: 1192: 1185:used by the 1173: 1158: 1143: 1137: 1120:Robert Tryon 1118:in 1938 and 1116:Joseph Zubin 1113: 1106: 1102: 1081: 1075: 1068: 1064: 1062: 1027: 979: 975: 971: 970: 838:PAC learning 525: 374: 369:Hierarchical 351: 301: 255: 249: 158: 11267:Data mining 11240:WikiProject 11155:Cartography 11117:Jurimetrics 11069:Reliability 10800:Time domain 10779:(Ljung–Box) 10701:Time-series 10579:Categorical 10563:Time-series 10555:Categorical 10490:(Bernoulli) 10325:Correlation 10305:Correlation 10101:Jarque–Bera 10073:Chi-squared 9835:M-estimator 9788:Asymptotics 9732:Sufficiency 9499:Interaction 9411:Replication 9391:Effect size 9348:Violin plot 9328:Radar chart 9308:Forest plot 9298:Correlogram 9248:Kendall's τ 8904:Categories 8852:Autoencoder 8807:Transformer 8675:Alex Graves 8623:OpenAI Five 8527:IBM Watsonx 8149:Convolution 8127:Overfitting 7356:(1): 1985. 5969:10481/84538 5562:Climatology 5372:communities 5172:phylogenies 2479:of cluster 2171:correlation 2081:clustering 1849:overfitting 1820:-means and 1229:Group model 992:statistical 982:) are more 722:Multi-agent 659:Transformer 558:Autoencoder 314:Naive Bayes 52:data mining 11256:Categories 11107:Demography 10825:ARMA model 10630:Regression 10207:(Friedman) 10168:(Wilcoxon) 10106:Normality 10096:Lilliefors 10043:Student's 9919:Resampling 9793:Robustness 9781:divergence 9771:Efficiency 9709:(monotone) 9704:Likelihood 9621:Population 9454:Stratified 9406:Population 9225:Dependence 9181:Count data 9112:Percentile 9089:Dispersion 9022:Arithmetic 8957:Statistics 8893:Technology 8746:EleutherAI 8705:Fei-Fei Li 8700:Yann LeCun 8613:Q-learning 8596:Decisional 8522:IBM Watson 8430:Midjourney 8322:TensorFlow 8169:Activation 8122:Regression 8117:Clustering 7734:NeuroImage 7268:1704.01036 7134:: 95–104. 6309:1110589522 6187:AAAI Press 5952:: 115265. 5783:2019-02-18 5754:References 5526:Typologies 5318:population 5246:genotyping 5202:(ESTs) or 5147:See also: 4555:Markedness 4088:Dice index 4058:Note that 3438:Rand index 3108:Rand index 2687:Dunn index 2258:See also: 2012:Mean-shift 1464:dendrogram 1423:Algorithms 1134:Definition 1082:botryology 1069:automatic 1065:clustering 976:clustering 707:Q-learning 605:Restricted 403:Mean shift 352:Clustering 329:Perceptron 257:regression 159:Clustering 154:Regression 10488:Logistic 10255:posterior 10181:Rank sum 9929:Jackknife 9924:Bootstrap 9742:Bootstrap 9677:Parameter 9626:Statistic 9421:Statistic 9333:Run chart 9318:Pie chart 9313:Histogram 9303:Fan chart 9278:Bar chart 9160:L-moments 9047:Geometric 8776:MIT CSAIL 8741:Anthropic 8710:Andrew Ng 8608:AlphaZero 8452:VideoPoet 8415:AlphaFold 8352:MindSpore 8306:SpiNNaker 8301:Memristor 8208:Diffusion 8184:Rectifier 8164:Batchnorm 8144:Attention 8139:Adversary 7992:0015-198X 7697:1088-9051 7650:0022-2836 7615:0020-0190 7564:1860-0980 7370:189915041 7226:Zimek, A. 7161:: 53–65. 7043:803401334 7007:915286380 6897:CiteSeerX 6732:CiteSeerX 6724:Zimek, A. 6673:CiteSeerX 6665:Zimek, A. 6618:CiteSeerX 6610:Zimek, A. 6571:CiteSeerX 6563:Zimek, A. 6520:CiteSeerX 6512:Zimek, A. 6450:CiteSeerX 6252:CiteSeerX 6224:CiteSeerX 6220:ACM Press 5978:0165-1781 5819:0096-851X 5326:customers 5322:consumers 5291:activity. 5278:PET scans 5248:platforms 5007:∑ 4966:∑ 4926:∑ 4891:∈ 4831:∈ 4704:≪ 4571:Chi Index 4486:precision 4482:G-measure 4435:precision 4282:⋅ 4232:formula: 3987:∪ 3966:∩ 3867:β 3841:β 3778:β 3742:⋅ 3733:β 3724:⋅ 3718:⋅ 3700:β 3685:β 3646:rate and 3644:precision 3502:precision 3484:≥ 3481:β 3458:F-measure 3075:∩ 3058:∈ 3042:∈ 3035:∑ 2919:anomalies 2869:centroids 2789:′ 2776:≤ 2770:≤ 2734:≤ 2722:≤ 2508:σ 2381:σ 2368:σ 2352:≠ 2324:∑ 2083:algorithm 1976:ε 1948:ε 1567:− 1034:distances 1030:algorithm 866:ECML PKDD 848:VC theory 795:ROC curve 727:Self-play 647:DeepDream 488:Bayes net 279:Ensembles 60:Paradigms 11202:Category 10895:Survival 10772:Johansen 10495:Binomial 10450:Isotonic 10037:(normal) 9682:location 9489:Blocking 9444:Sampling 9323:Q–Q plot 9288:Box plot 9270:Graphics 9165:Skewness 9155:Kurtosis 9127:Variance 9057:Heronian 9052:Harmonic 8884:Portals 8643:Auto-GPT 8475:Word2vec 8279:Hardware 8196:Datasets 8098:Concepts 7957:22655306 7949:19076414 7764:20933091 7715:11435409 7658:11743721 7529:36701919 7461:93003939 7437:: 1–17. 7202:(eds.). 7191:(2010). 7107:citation 6919:17218491 6866:Wcci Cec 6448:: 5–33. 6363:11323096 6161:Archived 6145:36920706 6119:(2011). 6099:10833328 5929:20:181–7 5835:(1939). 5595:See also 5455:cluster. 5265:Medicine 5212:genomics 3440:is that 3309:pairwise 2936:), such 2477:centroid 2236:indirect 2228:external 2224:internal 2136:big data 1739:-means++ 1721:-medoids 1377:outliers 1264:: Every 1050:data set 289:Boosting 138:Problems 11228:Commons 11175:Kriging 11060:Process 11017:studies 10876:Wavelet 10709:General 9876:Plug-in 9670:L space 9449:Cluster 9150:Moments 8968:Outline 8766:Meta AI 8603:AlphaGo 8587:PanGu-Σ 8557:ChatGPT 8532:Granite 8480:Seq2seq 8459:Whisper 8380:WaveNet 8375:AlexNet 8347:Flux.jl 8327:PyTorch 8179:Sigmoid 8174:Softmax 8039:General 7929:Bibcode 7802:1775181 7755:3008313 7572:5234703 7320:2288117 7285:2284239 6969:6935380 6927:6502291 6889:Bibcode 6881:Science 6868:. 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