Iteratively Reweighted Minimax-Concave Penalty Minimization for Accurate Low-rank Plus Sparse Matrix Decomposition.

Area of Science:

• Computer Vision
• Machine Learning
• Matrix Decomposition

Background:

• Low-rank plus sparse matrix decomposition (LSD) is crucial in computer vision and machine learning.
• Existing convex relaxation methods (nuclear norm, l1-norm) yield biased estimates.
• Nonconvex regularizers like weighted nuclear-norm and Schatten p-norm have heuristic weight-selection issues.

Purpose of the Study:

• To propose novel, adaptive weight-selection strategies for nonconvex regularizers in LSD.
• To introduce weighted minimax-concave penalty (WMCP) and weighted matrix gamma norm (WMGN) for improved LSD accuracy.
• To validate the effectiveness of these methods in video foreground-background separation.

Main Methods:

• Developed equivalent representations for WMCP and WMGN to enable adaptive weight selection.
• Employed the alternating direction method of multipliers (ADMM) for optimization.
• Introduced a novel iterative weight update strategy within the ADMM framework.

Main Results:

• The proposed WMCP and WMGN methods achieve accurate low-rank plus sparse matrix decomposition.
• The algorithms demonstrate descent properties and convergence guarantees.
• Outperformed benchmark techniques in foreground-background separation on standard datasets (I2R, CDnet 2012, BMC 2012).

Conclusions:

• The novel adaptive weight strategies for WMCP and WMGN offer significant improvements in LSD.
• These methods provide a robust and accurate solution for matrix decomposition tasks.
• Demonstrated practical effectiveness in real-world applications like video analysis.