Detection of Modal Clusters in High-dimensional Data

• Activity Number: 276
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Surajit Ray*+ and Bruce G. Lindsay
• Companies: University of North Carolina, Chapel Hill and Pennsylvania State University
• Keywords: modes ; bimodal ; dimension reduction ; modal cluster ; mixture

Abstract

Fitting a mixture model offers a primary data reduction through the number, location, and shape of its components, but in more complex settings we would like to know more about how the components interact to describe an overall pattern of density. In terms of subgroup structure for a two component mixture, we might create two competing hypotheses: either there are a homogeneous groups with normal shape, or one aggregated group having a more complex shape. We are interested determining how the aggregation of mixture components defines a modal cluster. This paper develops new tools for finding modal clusters, ones that are useful especially in high dimensions. For a unimodal density, concepts like skewness and kurtosis, heavy and light tails are used to describe shape. When the density is multimodal however, emphasis usually shifts to the number and location of modes. This is because the modes are often symptomatic of underlying population structures. Our investigation into the topography of a mixture of K=2 components D-variate normals yielded several interesting results.