Subspace Clustering with the Multivariate-t Distribution

Abstract: Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. In model-based clustering, a method called high-dimensional data clustering (HDDC) uses a family of Gaussian mixture models for clustering. HDDC is based on the idea that high-dimensional data usually exists in lower-dimensional subspaces; as such, an intrinsic dimension for each sub-population of the observed data can be estimated and cluster analysis can be performed in this lower-dimensional subspace. As a result, only a fraction of the total number of parameters need to be estimated and a computationally efficient parameter estimation scheme based on the EM algorithm was developed. This family of models has gained attention due to its superior classification performance compared to other families of mixture models; however, it still suffers from the usual limitations of Gaussian mixture model-based approaches. In this paper, a robust analogue of the HDDC approach is proposed. This approach, which extends the HDDC procedure to include the mulitvariate-t distribution, encompasses 28 models that rectify the aforementioned shortcomings of the HDDC procedure. Our tHDDC procedure is fitted to both simulated and real data sets and is compared to the HDDC procedure using an image reconstruction problem that arose from satellite imagery of Mars' surface.