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Unsupervised classification and analysis of objects described by nonparametric probability distributions
Author(s) -
Emilion Richard
Publication year - 2012
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11160
Subject(s) - dirichlet distribution , nonparametric statistics , consistency (knowledge bases) , mathematics , hierarchical dirichlet process , dirichlet process , probability distribution , pattern recognition (psychology) , computer science , artificial intelligence , statistics , bayesian probability , mathematical analysis , boundary value problem
Various objects can be summarily described by probability distributions: groups of raw data, paths of stochastic processes, neighborhoods of an image pixel and so on. Dealing with nonparametric distributions, we propose a method for classifying such objects by estimating a finite mixture of Dirichlet distributions when the observed distributions are assumed to be outcomes of a finite mixture of Dirichlet processes. We prove the consistency of such a classification by using the mutual singularity of two distinct Dirichlet processes and the martingale convergence theorem. Moreover, this consistency allows us to use some standard data analysis and statistical methods for analyzing the class labels of these objects. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012