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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).
Fuzzy clustering (also referred to as soft clustering or soft k-means) is a form of clustering in which each data point can belong to more than one cluster.. Clustering or cluster analysis involves assigning data points to clusters such that items in the same cluster are as similar as possible, while items belonging to different clusters are as dissimilar as possible.
When clustering text databases with the cover coefficient on a document collection defined by a document by term D matrix (of size m×n, where m is the number of documents and n is the number of terms), the number of clusters can roughly be estimated by the formula where t is the number of non-zero entries in D. Note that in D each row and each ...
Let (G, *) be a group and A a fuzzy subset of G. Then A is a fuzzy subgroup of G if for all x, y in G, A(x*y −1) ≥ min(A(x), A(y −1)). A similar generalization principle is used, for example, for fuzzification of the transitivity property. Let R be a fuzzy relation on X, i.e. R is a fuzzy subset of X × X.
Model-based clustering was first invented in 1950 by Paul Lazarsfeld for clustering multivariate discrete data, in the form of the latent class model. [41] In 1959, Lazarsfeld gave a lecture on latent structure analysis at the University of California-Berkeley, where John H. Wolfe was an M.A. student. This led Wolfe to think about how to do the ...
The information bottleneck method is a technique in information theory introduced by Naftali Tishby, Fernando C. Pereira, and William Bialek. [1] It is designed for finding the best tradeoff between accuracy and complexity (compression) when summarizing (e.g. clustering) a random variable X, given a joint probability distribution p(X,Y) between X and an observed relevant variable Y - and self ...
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A fuzzy set is a pair (,) where is a set (often required to be non-empty) and : [,] a membership function. The reference set (sometimes denoted by or ) is called universe of discourse, and for each , the value () is called the grade of membership of in (,).