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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).
(top) Initial cluster assignment. (middle) The graph after the first step 2, in which (in order) the pink, green, yellow, red, black, white, and blue nodes were selected. (bottom) The graph after a second step 2, in which the green and white nodes were selected, with the order of the remaining nodes after that not important.
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]
Two points p and q are density-connected if there is a point o such that both p and q are reachable from o. Density-connectedness is symmetric. A cluster then satisfies two properties: All points within the cluster are mutually density-connected. If a point is density-reachable from some point of the cluster, it is part of the cluster as well.
Ward's minimum variance method can be defined and implemented recursively by a Lance–Williams algorithm. The Lance–Williams algorithms are an infinite family of agglomerative hierarchical clustering algorithms which are represented by a recursive formula for updating cluster distances at each step (each time a pair of clusters is merged).
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 .
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 ...
At each step one has to build and search a matrix. Initially the Q {\displaystyle Q} matrix is size n × n {\displaystyle n\times n} , then the next step it is ( n − 1 ) × ( n − 1 ) {\displaystyle (n-1)\times (n-1)} , etc. Implementing this in a straightforward way leads to an algorithm with a time complexity of O ( n 3 ) {\displaystyle O ...