Simplified stress and simplified silhouette coefficient to a faster quality evaluation of multidimensional projection techniques and feature spaces

Abstract

Several multidimensional projection techniques have been proposed in literature over the last years. The quality of those techniques can be evaluated based on the dimensionality reduction or the clusters quality. The first evaluation aim to verify if the similarities from multidimensional space are preserved in projected space. While the second evaluation aim to verify if instances from a same class are placed in a same cluster in projected space. Respectively, Stress and Silhouette Coefficient are the main measures to quality evaluations. In this paper we present two new approaches - named Simplified Stress and Simplified Silhouette Coefficient - to speed up the computation of measures, enabling a faster evaluation of multidimensional projection techniques and feature spaces. We present experiments showing the high correlation between results obtained using original approaches and results obtained with those proposed in this paper. In addition, we show how to use Simplified Silhouette Coefficient to perform a fast feature space evaluation and selection.