Title: Bayes Clusterer

		Edward R. Dougherty and Marcel Brun
	       Department of Electrical Engineering
	               Texas A&M University
		     Email: edward@ee.tamu.edu


Abstract:
The theory of pattern classification is based on designing an operator on 
feature random variables that outputs a label. There exists a joint 
feature-label distribution whose conditional distributions with respect to 
the labels determine the feature classes. Within this framework, there exists 
an error criterion, an optimal (Bayes) classifier, and a theory of learning. 
For clustering, there has historically been little theory; rather, it has 
developed as a collection of ad hoc algorithms applied to collections of data 
points. Not being grounded on a distributional theory, it has lacked an error 
criterion, except in the case of some model-based approaches. Consequently, 
optimality has been absent. Moreover, there has been no learning, just the 
application of an algorithm based on some heuristic understanding of 
empirical relations among the data. This talk discusses a mathematical theory 
of cluster operators that includes a general error criterion, optimality, and 
learning. It focuses on the distributional setting and the Bayes (optimal) 
clusterer.