Clustering of High-Dimensional Data via Finite Mixture Models

Abstract

Finite mixture models are being commonly used in a wide range of applications in practice concerning density estimation and clustering. An attractive feature of this approach to clustering is that it provides a sound statistical framework in which to assess the important question of how many clusters there are in the data and their validity. We review the application of normal mixture models to high-dimensional data of a continuous nature. One way to handle the fitting of normal mixture models is to adopt mixtures of factor analyzers. They enable model-based density estimation and clustering to be undertaken for high-dimensional data, where the number of observations n is not very large relative to their dimension p. In practice, there is often the need to reduce further the number of parameters in the specification of the component-covariance matrices. We focus here on a new modified approach that uses common component-factor loadings, which considerably reduces further the number of parameters. Moreover, it allows the data to be displayed in low-dimensional plots.