Robust Matrix Factorization by Majorization Minimization.

Area of Science:

• Computer Vision
• Machine Learning
• Optimization

Background:

• Low-rank matrix factorization is crucial for computer vision tasks.
• Existing methods struggle with missing data, outliers, and lack theoretical guarantees.
• Non-convexity and non-smoothness pose significant challenges in these methods.

Purpose of the Study:

• To develop a scalable and robust algorithm for norm-based low-rank matrix factorization.
• To address limitations of existing methods regarding missing data, outliers, and convergence guarantees.
• To provide theoretical convergence proofs for the proposed optimization technique.

Main Methods:

• Application of the Majorization Minimization (MM) technique.
• Upper bounding the objective function with a strongly convex surrogate at each iteration.
• Minimizing the surrogate to ensure sufficient decrease in the objective function.

Main Results:

• The proposed algorithm demonstrates strong convergence properties, guaranteeing limit points are stationary points without extra assumptions.
• Experimental results on synthetic and real datasets confirm the algorithm's effectiveness and robustness.
• The method achieves competitive speed compared to existing approaches.

Conclusions:

• The Majorization Minimization technique provides an effective solution for robust low-rank matrix factorization.
• The algorithm offers superior convergence guarantees and practical performance.
• This work advances the state-of-the-art in handling challenging data conditions in matrix factorization.