Heterogeneous Sufficient Dimension Reduction and Subspace Clustering

Abstract

Scientific and engineering applications are often heterogeneous, making it beneficial to account for latent clusters or sub-populations when learning low-dimensional subspaces in supervised learning, and vice versa. In this paper, we combine the concept of subspace clustering with model-based sufficient dimension reduction and thus generalize the sufficient dimension reduction framework from homogeneous regression setting to heterogeneous data applications. In particular, we propose the mixture of principal fitted components (mixPFC) model, a novel framework that simultaneously achieves clustering, subspace estimation, and variable selection, providing a unified solution for high-dimensional heterogeneous data analysis. We develop a group Lasso penalized expectation-maximization (EM) algorithm and obtain its non-asymptotic convergence rate. Through extensive simulation studies, mixPFC demonstrates superior performance compared to existing methods across various settings. Applications to real world datasets further highlight its effectiveness and practical advantages.