Tensor Low-Rank Representation for Data Recovery and Clustering.

Area of Science:

• Multi-way data analysis
• Tensor decomposition
• Machine learning

Background:

• Tensor data analysis is increasingly important in various fields.
• Existing methods struggle with corrupted data and accurate clustering.
• Low-rank representation is a promising approach for data analysis.

Purpose of the Study:

• To develop a Tensor Low-Rank Representation (TLRR) method.
• To achieve exact recovery of clean tensor data with intrinsic low-rank structure.
• To accurately cluster tensor data with provable performance guarantees.

Main Methods:

• Developed a novel Tensor Low-Rank Representation (TLRR) method.
• Proposed efficient convex programming for optimizing the TLRR objective function.
• Introduced two dictionary construction methods: simple TLRR (S-TLRR) and robust TLRR (R-TLRR).

Main Results:

• TLRR exactly recovers clean tensor data from arbitrary sparse corruptions under mild conditions.
• TLRR accurately verifies true origin tensor subspaces for precise clustering.
• Experimental results show superior performance, efficiency, and robustness over state-of-the-art methods.

Conclusions:

• TLRR is the first method to exactly recover and accurately cluster tensor data with intrinsic low-rank structure.
• TLRR offers provable performance guarantees and is optimized via efficient convex programming.
• S-TLRR and R-TLRR effectively handle slightly and severely corrupted data, respectively.