A Multilinear Least-Squares Formulation for Sparse Tensor Canonical Correlation Analysis

Abstract

Tensor data are becoming important recently in various applications, e.g., image and video recognition, which pose new challenges for data modeling and analysis approaches, such as high-order relations of large complexity, varying data scale and gross noise. In this paper, we consider the problem of sparse canonical correlation analysis for arbitrary tensor data. Although several methods have been proposed for this task, there are still limitations hindering its practical applications. To this end, we present a general Sparse Tensor Canonical Correlation Analysis (gSTCCA) method from a multilinear least-squares perspective. Specifically, we formulate the problem as a constrained multilinear least-squares problem with tensor-structured sparsity regularization based on CANDECOMP/PARAFAC (CP) decomposition. Then we present a divide-and-conquer deflation approach to tackle the problem by successive rank-one tensor estimation of the residual tensors, where the overall model is broken up into a set of unconstrained linear least-squares problems that can be efficiently solved. Through extensive experiments conducted on five different datasets for recognition tasks, we demonstrate that the proposed method achieves promising performance compared to the SOTA vector- and tensor-based canonical correlation analysis methods in terms of classification accuracy, model sparsity, and robustness to missing and noisy data. The code is publicly available at https://github.com/junfish/gSTCCA.