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Iterative Optimization and Simplification of Hierarchical Clusterings

Doug Fisher

Department of Computer Science
Box 1679, Station B
Vanderbilt University
Nashville, TN 37235 USA

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search strategy should consistently construct clusterings of high quality, but be computationally inexpensive as well. In general, we cannot have it both ways, but we can partition the search so that a system inexpensively constructs a `tentative' clustering for initial examination, followed by iterative optimization, which continues to search in background for improved clusterings. Given this motivation, we evaluate an inexpensive strategy for creating initial clusterings, coupled with several control strategies for iterative optimization, each of which repeatedly modifies an initial clustering in search of a better one. One of these methods appears novel as an iterative optimization strategy in clustering contexts. Once a clustering has been constructed it is judged by analysts -- often according to task-specific criteria. Several authors have abstracted these criteria and posited a generic performance task akin to pattern completion, where the error rate over completed patterns is used to `externally' judge clustering utility. Given this performance task, we adapt resampling-based pruning strategies used by supervised learning systems to the task of simplifying hierarchical clusterings, thus promising to ease post-clustering analysis. Finally, we propose a number of objective functions, based on attribute-selection measures for decision-tree induction, that might perform well on the error rate and simplicity dimensions.

Acknowledgements: I thank Sashank Varma, Arthur Nevins, and Diana Gordon for comments on the paper. The reviewers and editor supplied extensive and helpful comments. This work was supported by grant NAG 2-834 from NASA Ames Research Center. A very abbreviated discussion of some of this article's results appear in Fisher [1995], published by AAAI Press.

next up previous
Next: Introduction

Douglas H. Fisher
Sat Mar 30 11:37:23 CST 1996