Trace Norm Regularized CANDECOMP/PARAFAC Decomposition With Missing Data.

Area of Science:

• Computer Science
• Data Science
• Signal Processing

Background:

• Low-rank tensor completion (LRTC) is crucial in computer vision, data mining, and signal processing.
• Existing trace norm minimization algorithms for LRTC are computationally expensive due to repeated large matrix singular value decompositions.

Purpose of the Study:

• To develop a computationally efficient and scalable method for low-rank tensor completion.
• To introduce a novel approach that simultaneously performs tensor decomposition and completion.

Main Methods:

• Formulated a factor matrix rank minimization model relating factor matrix rank to tensor mode-n rank.
• Introduced a tractable relaxation for rank minimization, creating a convex combination of smaller matrix trace norm minimization problems.
• Developed an efficient algorithm using the alternating direction method of multipliers (ADMM) for solving the proposed model.

Main Results:

• The proposed trace norm regularized CANDECOMP/PARAFAC decomposition (TNCP) method effectively handles tensor decomposition and completion.
• Experimental results on synthetic and real-world data demonstrate the superiority of TNCP.
• TNCP shows significant speed improvements and better scalability compared to state-of-the-art methods.

Conclusions:

• TNCP offers an effective and efficient solution for low-rank tensor completion problems.
• The method's computational advantages make it suitable for large-scale applications.
• TNCP represents a significant advancement in tensor completion techniques.