Simultaneous tensor decomposition and completion using factor priors.

Area of Science:

• Data Science
• Applied Mathematics
• Machine Learning

Background:

• Matrix completion research shows significant real-world success.
• Tensor completion, an extension of matrix completion, is gaining research traction.
• Existing tensor completion methods face challenges with increasing missing data.

Purpose of the Study:

• To develop a novel method for simultaneous tensor completion and model structure capture.
• To address limitations of existing factorization and completion schemes in handling missing data.
• To leverage factor priors for enhanced tensor recovery and model interpretation.

Main Methods:

• Proposed Simultaneous Tensor Decomposition and Completion (STDC) method.
• Combined rank minimization with Tucker model decomposition.
• Utilized factor priors inherent in real-world tensor objects.

Main Results:

• Empirically verified algorithm convergence on synthetic data.
• Demonstrated effectiveness on various real-world datasets.
• Outperformed state-of-the-art methods in multilinear model analysis and visual data completion.

Conclusions:

• The STDC method accurately estimates model factors and missing entries.
• The approach shows significant potential for tensor-based applications.
• STDC offers a robust solution for complex tensor completion tasks.