Subspace clustering with the multivariate-t distribution

Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. One approach, 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 needs to be estimated. 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, e.g., these models are sensitive to outlying or spurious points. In this paper, a robust analog of the HDDC approach is proposed. This approach, which extends the HDDC procedure to the multivariate-t distribution, encompasses 28 models that rectify the aforementioned shortcoming of the HDDC procedure. Our tHDDC procedure is compared to the HDDC procedure using both simulated and real data sets, which includes an image reconstruction problem that arose from satellite imagery of the surface of Mars.