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Bayes clustering operators for known random labeled point processes

Abstract:

There is a widespread belief that clustering is inherently subjective. To quote A. K. Jain, 'As a task, clustering is subjective in nature. The same dataset may need to be partitioned differently for different purposes.' One is then left with a number of questions: Where do clustering algorithms account for statistical properties of the sampling procedure? How can one address the ability of a clusterer to make inferences without a definition of its predictive capacity? This work develops a probabilistic theory of clustering that fully parallels the well-developed Bayes decision theory for classification, making it possible to address these questions and transform clustering from a subjective activity to an objective operation. © 2013 IEEE.