GoDec+: Fast and Robust Low-Rank Matrix Decomposition Based on Maximum Correntropy

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Low-rank matrix decomposition is crucial for data analysis.
• Existing algorithms like GoDec are sensitive to noise and corruptions.
• Handling diverse corruptions remains a challenge in matrix decomposition.

Purpose of the Study:

• To develop a more robust and faster low-rank decomposition algorithm.
• To address matrices composed of low-rank components and unknown corruptions.
• To introduce correntropy as a robust measure for data corruptions.

Main Methods:

• Introduced correntropy, a robust local similarity measure, to describe corruptions.
• Developed GoDec+, a low-rank decomposition algorithm based on maximum correntropy criterion (MCC).
• Utilized half-quadratic optimization and a greedy bilateral paradigm for the solution.

Main Results:

• GoDec+ demonstrates efficiency and robustness against Gaussian noise, Laplacian noise, salt & pepper noise, and occlusion.
• Achieved state-of-the-art performance in subspace clustering on benchmark datasets (Hopkins 155, Extended Yale B).
• Successfully applied GoDec+ to classification and subspace clustering tasks, showing effectiveness and robustness.

Conclusions:

• GoDec+ offers a significant improvement over existing methods for low-rank decomposition under corruptions.
• The MCC-based approach provides enhanced robustness and efficiency.
• The algorithm's applications in classification and subspace clustering yield effective and reliable results.