Second-Order Convergence of Regularized ALS for Tensor CP Approximation
Abstract
The regularized alternating least squares (ALS) is a widely used method for computing the CP decomposition of tensors. Existing convergence analyses for the regularized ALS are limited to first-order stationary points. In this work, we study its second-order convergence and prove that, with random initialization, the regularized ALS almost surely avoids strict saddle points. These results provide stronger theoretical guarantees for the effectiveness of regularized ALS in practical tensor approximation tasks.
Fields of Study & Subjects
Tensor decomposition and applications
Sparse and Compressive Sensing Techniques
Stochastic Gradient Optimization Techniques
Publication details
- Journal / source
- IEEE Signal Processing Letters
- Volume
- 33
- Pages
- 619–623
- Publication date
- 1 January 2026