Sparse Tensor CCA via Manifold Optimization for Multi-View Learning

Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization of individual structures and lack algorithmic convergence guarantees. In order to deal with these challenges, we propose a novel sparse TCCA model called STCCA-L, which integrates sparse regularization of canonical matrices and Laplacian regularization of multi-order graphs into the TCCA framework, thereby effectively exploiting the geometric structure of individual views. To solve this non-convex model, we develop an efficient alternating manifold proximal gradient algorithm based on manifold optimization, which avoids computationally expensive full tensor decomposition and leverages a semi-smooth Newton method for resolving the subproblem. Furthermore, we rigorously prove the convergence of the algorithm and analyze its complexity. Experimental results on eight benchmark datasets demonstrate the superior classification performance of the proposed method. Notably, on the 3Sources dataset, it achieves improvements of at least 4.50\% in accuracy and 6.77\% in F1 score over competitors. Our code is available at https://github.com/zhudafa/STCCA-L.