Theoretical and Experimental Analyses of Tensor-Based Regression and Classification
This work addresses the need for more effective learning methods in data analysis, but it appears incremental as it builds on existing tensor norms and optimization techniques.
The authors tackled the problem of improving regression and classification by using tensor-based methods with various regularization norms, and demonstrated their superiority over vector- and matrix-based methods through extensive experiments.
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method of multipliers, which is computationally efficient when the number of training samples is moderate. We then theoretically derive an excess risk bound for each tensor norm and clarify their behavior. Finally, we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor-based learning methods over vector- and matrix-based learning methods.