Riemannian Optimization for Sparse Tensor CCA

Tensor canonical correlation analysis (TCCA) has received significant attention due to its ability to effectively preserve the geometric structure of high-order data. However, existing methods generally rely on tensor decomposition techniques with high computational complexity, which severely limits their application in large-scale datasets. In this paper, a modified method, TCCA-L, is proposed, which integrates sparse regularization and Laplacian regularization. An alternating manifold proximal gradient algorithm is designed based on Riemannian manifold theory. The algorithm avoids the traditional tensor decomposition and combines with the semi-smooth Newton algorithm to solve the subproblem, thus significantly improving the computational efficiency. Furthermore, the global convergence of the sequence generated by the algorithm is established, providing a solid theoretical foundation for its convergence. Numerical experiments demonstrate that TCCA-L outperforms traditional methods in both classification accuracy and running time.