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Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters).
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
In complete-linkage clustering, the link between two clusters contains all element pairs, and the distance between clusters equals the distance between those two elements (one in each cluster) that are farthest away from each other. The shortest of these links that remains at any step causes the fusion of the two clusters whose elements are ...
Biclustering, block clustering, [1] [2] Co-clustering or two-mode clustering [3] [4] [5] is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix. The term was first introduced by Boris Mirkin [ 6 ] to name a technique introduced many years earlier, [ 6 ] in 1972, by John A. Hartigan .
Much of the model-based clustering software is in the form of a publicly and freely available R package. Many of these are listed in the CRAN Task View on Cluster Analysis and Finite Mixture Models. [34] The most used such package is mclust, [35] [36] which is used to cluster continuous data and has been downloaded over 8 million times. [37]
In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical clustering.These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form larger clusters.
Automatic clustering algorithms are algorithms that can perform clustering without prior knowledge of data sets. In contrast with other cluster analysis techniques, automatic clustering algorithms can determine the optimal number of clusters even in the presence of noise and outlier points. [1] [needs context]
At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any two clusters and , each of size (i.e., cardinality) | | and | |, is taken to be the average of all distances (,) between pairs of objects in and in , that is, the mean distance between elements of each cluster: