JSM 2004 - Toronto

Abstract #302076

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Activity Number: 425
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract - #302076
Title: Efficient Clustering for Principal Components
Author(s): Bruce Barrett*+ and Wade Watkins
Companies: University of Alabama and University of Alabama
Address: Information Systems, Statistics, and Mgt. Science, Tuscaloosa, AL, 35487-0226,
Keywords: clustering ; branch and bound ; principal components
Abstract:

Traditional hierarchical methods for clustering variables are typically not aimed at optimizing any particular objective function. Rather, they provide for groupings tied to the more general "similarity" information contained in the correlation matrix. However, in some applications, clustering is a preliminary step for some secondary analysis with quite specific criteria. For example, if the number of variables, p, is large, clustering might be employed prior to a principal components analysis, or as a surrogate for factor analysis. In these instances, we may wish to achieve the cluster configuration that maximizes the sum of the largest k / P eigenvalues for the k correlation submatrices, indexed by the clusters. Optimization necessarily involves consideration of each possible partitioning. We present an algorithm for an efficient search, based on a branch-and-bound procedure and compare this result with that arrived at by various hierarchical methods.

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