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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.
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.
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]
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 .
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:
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 ...
The canopy clustering algorithm is an unsupervised pre-clustering algorithm introduced by Andrew McCallum, Kamal Nigam and Lyle Ungar in 2000. [1] It is often used as preprocessing step for the K-means algorithm or the hierarchical clustering algorithm.