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FocalPoint: Two-Stage k-Means Method

for Optimum ESS Cluster Models

David Wishart

Department of Management, University of St. Andrews
St Katharine's West, The Scores, St. Andrews KY16 9AL, Scotland

The paper describes FocalPoint, a two-stage k-means method to search for optimum ESS cluster models.

The first stage completes k-means analysis with six different starting strategies and randomized trials, to test the sensitivity of the starting solution and case order.  Differential variable and case weights can be specified, outliers and intermediate cases can be removed, and clustering can be around cluster means or exemplars. An exact relocation test on the Euclidean Sum of Squares (ESS) assures convergence.

The top solutions found at the first stage are saved, ordered by goodness-of-fit, and their reproducibility is estimated.  The second stage involves cluster model profiling, evaluation, selection, and calibration.  Variable weights can be revised by t-tests on cluster means or F-tests on variances, so as to emphasise the most discriminating variables.  When a final cluster model has been chosen, it can be summarizing by hierarchical cluster analysis, with optimal cluster ordering, and outlier assignment.

FocalPoint will be illustrated by a market segmentation of malt whiskies (presentation to precede the banquet).  A trial version is available with ClustanGraphics4 on the CLASS CD, distributed with the Journal of Classification, v 17(1), May 2000. .