Learning High-Order Multi-View Representation by New Tensor Canonical Correlation Analysis

Canonical correlation analysis (CCA) has attracted great interest in multi-view representation. However, most of the CCA methods heavily rely on the matrix structure, which may neglect the prior geometric information in high-order data. To deal with the above issue, we first propose a novel tensor CCA formulation with orthogonality, called TCCA-O, based on the Tucker decomposition to preserve the orthogonality. Then, we incorporate a structured sparse regularization term into the TCCA-O, called TCCA-OS, to improve feature representation. In addition, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm to solve TCCA-OS and conduct numerical comparisons on four public datasets. The results validate the advantages of the proposed methods in terms of classification accuracy, parameter sensitivity, noise robustness, and model stability. In particular, TCCA-O and TCCA-OS improve the classification accuracy by at least 10.03% and 10.36%, respectively, over the state-of-the-art CCA methods on the Caltech101-7 dataset.