Covariance-Guided Mixture Probabilistic Principal Component Analysis (C-MPPCA)

To extract information from high-dimensional data efficiently, visualization tools based on data projection methods have been developed and shown useful. However, a single two-dimensional visualization is often insufficient for capturing all or most interesting structures in complex high-dimensional datasets. For this reason, Tipping and Bishop developed mixture probabilistic principal component analysis (MPPCA) that separates data into multiple groups and enables a unique projection per group; that is, one probabilistic principal component analysis (PPCA) data visualization per group. Because the group labels are assigned to observations based on their high-dimensional coordinates, MPPCA works well to reveal homoscedastic structures in data that differ spatially. In the presence of heteroscedasticity, however, MPPCA may still mask noteworthy data structures. We propose a new method called covariance-guided MPPCA (C-MPPCA) that groups subsets of observations based on covariance, not locality, and, similar to MPPCA, displays them using PPCA. PPCA projects data in the dimensions with the highest variances, thus grouping by covariance makes sense and enables some data structures to be visible that were masked originally by MPPCA. We demonstrate the performance of C-MPPCA in an extensive simulation study. We also apply C-MPPCA to a real world dataset. Supplementary materials for this article are available online.