Information and Entropy in Cluster Analysis

摘要: Cluster analysis provides methods for subdividing a set of objects into suitable number ‘classes’, ‘groups’, or ‘types’ C 1,…,C m such that each class is as homogeneous possible and different classes are sufficiently separated. This paper shows how entropy information measures have been can be used in this framework. We present several probabilistic clustering approaches which related to, lead criteria g(C) selecting an optimum partition = (C ) n data vectors, qualitative quantitative data, assuming loglinear, logistic, normal distribution models, together with appropriate iterative algorithms. A new partitioning problem considered Section 5 where we look dissection (discretization) arbitrary sample space Y (e.g. R p 0,1 the o—divergence I c (P 0, P 1) between two discretized distributions o i ), 1(C (i 1,…, m) will maximized (e.g., Kullback-Leibler’s discrimination X 2 noncentrality parameter). conclude some comments on classes, e.g., by using Akaike’s criterion AIC its modifications.