ABSTRACT OF THE DISSERTATION Statistical Strategies for Scaling and Weighting Variables for Cluster Analysis

Cluster analysis (CA) is a generic name for an array of quantitative methods, the applications of which are found in numerous fields ranging from astronomy and biology to finance and psychology. Though the intuitive idea of clustering is clear enough, the details of actually carrying out such an analysis entail many unresolved conceptual problems. Multivariate data, often poses a problem, in that the variables are not commensurate. Since the outcome of a CA is sensitive to the scales of measurement of the input data, many practitioners resort to standardizing the data prior to the analysis. Hence, the scaling of such multivariate data prior to CA is important as a preprocessing step. Autoscaling, is one such näıve approach. Although it is a widely used procedure to standardize variables in some major point and click statistical software packages, it ignores the inherent cluster structure and actually proves counterproductive. This dissertation is broadly divided into two parts- Univariate and Multivariate strategies. The first part addresses some univariate scaling and weighting approaches. In an attempt to put all variables on the same footing, we propose some intuitive strate-gies which we call equalizers. In addition, we consider letting the data suggest weight