Bayes clustering operators for known random labeled point processes

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.