Efficient l1 -norm-based low-rank matrix approximations for large-scale problems using alternating rectified gradient...

Area of Science:

• Computer Vision
• Image Processing
• Matrix Approximation

Background:

• Conventional low-rank matrix approximation, often using the l2-norm (Frobenius norm) and Principal Component Analysis (PCA), struggles with outlier-contaminated data.
• The l2-norm's sensitivity to outliers, including missing data, leads to poor approximation quality in real-world scenarios.
• Existing robust methods based on the l1-norm are computationally intensive and memory-demanding for high-dimensional data.

Purpose of the Study:

• To develop efficient low-rank factorization methods utilizing the l1-norm for improved robustness.
• To address the computational and memory limitations of current l1-norm based robust matrix approximation techniques.
• To demonstrate the efficiency and robustness of the proposed methods in computer vision and image processing applications.

Main Methods:

• Proposed two novel low-rank factorization methods based on the l1-norm.
• Employed the alternating rectified gradient method to determine projection and coefficient matrices.
• Applied the methods to various low-rank matrix approximation problems.

Main Results:

• The proposed methods demonstrated significant efficiency in execution time compared to state-of-the-art techniques.
• Achieved robust performance in reconstruction, effectively handling data with outliers.
• Outperformed existing methods in both speed and accuracy for low-rank matrix approximation tasks.

Conclusions:

• The developed l1-norm based low-rank factorization methods offer an efficient and robust alternative for computer vision and image processing.
• These methods provide a practical solution for handling outlier-prone data in high-dimensional settings.
• The alternating rectified gradient approach enables efficient computation without compromising approximation quality.