Clustering of High-Dimensional Data via Factor Models

• Activity Number: 209
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Geoffrey John McLachlan*+
• Companies: University of Queensland
• Keywords: High-dimensional data ; Clustering ; Normal mixture models ; Factor models ; Number of clusters

Abstract

There has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarray-based genomics and other high-throughput experimental approaches. Hence there has been increasing attention given not only in bioinformatics and machine learning, but also in mainstream statistics, to the analysis of complex data in this situation where n is small relative to p. In this talk, we focus on the clustering of high-dimensional data, using normal mixture models. Their use in this context is not straightforward, as the normal mixture model is a highly parameterized one with each component-covariance matrix consisting of p(p+1)/2 distinct parameters in the unrestricted case. Hence some restrictions must be imposed and/or a variable selection method applied beforehand. We shall focus on the use of factor models that reduce the number of parameters in the specification of the component-covariance matrices. We also consider the problem of assessing the significance of groups in high-dimensional data using a resampling approach.