Bayesian Low-Tubal-Rank Robust Tensor Factorization with Multi-Rank Determination.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Robust tensor factorization decomposes tensors into low-rank and sparse components.
• Existing methods struggle with preserving low-rank structures and determining tensor rank.
• Challenges include modeling power and inferring the trade-off between components.

Purpose of the Study:

• To propose a fully Bayesian approach for robust tensor factorization.
• To automatically determine tensor rank and the balance between low-rank and sparse components.
• To enhance the modeling power for preserving low-rank structures.

Main Methods:

• A generalized sparsity-inducing prior is introduced.
• A low-tubal-rank model is adapted in a generative manner.
• Variational inference is employed for model estimation, with frequency domain reformulation for efficiency.

Main Results:

• The proposed method effectively preserves low-rank structures.
• Automatic determination of tensor rank and component trade-offs is achieved.
• Superior performance in image denoising and background modeling demonstrated.

Conclusions:

• The Bayesian robust tensor factorization method offers significant improvements.
• Effective multi-rank determination and enhanced performance in applications.
• Addresses limitations of existing tensor factorization techniques.