Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

Area of Science:

• Machine Learning
• Applied Mathematics
• Data Science

Background:

• Low-rank tensor completion (LRTC) is widely used but computationally expensive for large datasets.
• Existing methods face scalability issues, limiting their practical application.

Purpose of the Study:

• To develop a computationally efficient LRTC method for large-scale problems.
• To improve the speed and accuracy of tensor learning and decomposition.

Main Methods:

• Proposed a novel core tensor trace-norm minimization (CTNM) method.
• Leveraged the equivalence between low-rank tensor trace norm and its core tensor trace norm.
• Developed an efficient alternating direction augmented Lagrangian method for optimization.

Main Results:

• CTNM achieves significantly lower computational complexity than traditional tensor trace-norm minimization (TNM).
• Requires fewer observations for reliable tensor recovery: O((R^N+NRI)log(sqrt(I^N))) vs. O(rI^(N-1)).
• Demonstrated superior accuracy and orders-of-magnitude speed improvement in extensive experiments.

Conclusions:

• CTNM offers a highly efficient and accurate solution for large-scale LRTC.
• The method effectively reduces computational burden while maintaining or improving performance.
• Presents a promising advancement for tensor learning and decomposition applications.