Strong Consistency of Prototype Based Clustering in Probabilistic Space

2010/04/19 by Vladimir Nikulin, Geoffrey J. McLachlan, Nikulin, Vladimir +1 · 1 citation
Computer Science · Mathematics · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (stat.ML) #stat.ML

paper · pdf · doi:10.48550/arxiv.1004.3101

arxiv created 2010/04/19 · openalex publication_date 2010/04/19 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullback-Leibler divergence which may be regarded as a special case within the Clustering Minimisation framework. Also, we propose clustering regularization restricting creation of additional clusters which are not significant or are not essentially different comparing with existing clusters.

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