Third-order tensor ridge regression based on tensor-product under general orthogonal transformation
Abstract
In this work, a novel tensor-to-tensor ridge regression model is introduced based on the tensor-tensor product (T-product), which extends the traditional matrix regression to tensor case. To estimate the coefficient tensor, the model integrates ridge penalty and tensor nuclear norm constraints to avoid overfitting and exploit multi-dimensional structural information, thereby preserving the intrinsic correlations in high-dimensional data. To solve the resulting optimization problem, we develop an easy-to-operate and effective algorithm with guaranteed convergence. Numerical experiments on both synthetic and real datasets demonstrate that the proposed method achieves superior performance in terms of prediction accuracy and computational efficiency.
Fields of Study & Subjects
Tensor decomposition and applications
Sparse and Compressive Sensing Techniques
Stochastic Gradient Optimization Techniques
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 27
- Issue
- 0
- Pages
- 143–163
- Publication date
- 1 January 2026