Kernel Bayesian tensor ring decomposition for multiway data recovery.

Area of Science:

• Machine Learning
• Data Science
• Signal Processing

Background:

• Tensor ring (TR) decomposition is a key method for tensor completion.
• Existing probabilistic TR methods often fail to incorporate side information.
• There's a need for methods that leverage auxiliary data for improved tensor completion.

Purpose of the Study:

• To propose a novel tensor completion method, variational inference-based kernel Bayesian TR (VKBTR).
• To integrate side information, low-rankness, and sparse learning into TR decomposition.
• To enable automatic TR rank selection and leverage intrinsic data properties.

Main Methods:

• Developed VKBTR by incorporating kernel matrices into TR factors.
• Introduced a sparsity-inducing hierarchical prior for automatic rank selection.
• Utilized variational inference for effective posterior parameter updates.

Main Results:

• VKBTR significantly improves tensor completion performance across various datasets (synthetic, images, video).
• The method effectively leverages side information and data smoothness (e.g., in images/videos).
• VKBTR outperforms existing state-of-the-art tensor completion methods.

Conclusions:

• VKBTR offers a powerful framework for tensor completion by integrating side information and kernel methods.
• The proposed approach enhances accuracy and enables automatic rank determination.
• VKBTR demonstrates superior performance, particularly when side information is available.