Low Rank Matrix Recovery via Robust Outlier Estimation

Area of Science:

• Data Science
• Machine Learning
• Statistics

Background:

• High-dimensional data often contain outliers and noise, complicating the recovery of underlying low-dimensional structures.
• Outliers, unlike small noises, pose a significant threat to data recovery accuracy due to their arbitrary magnitudes.

Purpose of the Study:

• To develop a robust method for outlier estimation in low-rank matrix recovery.
• To integrate outlier screening and matrix recovery into a unified framework.

Main Methods:

• Proposed a robust outlier estimate method named ROUTE.
• Formulated outlier screening and recovery into a unified framework.
• Developed two optimizers: ROUTE-BCD (block coordinate descent) and ROUTE-ADMM (alternating direction method of multipliers).

Main Results:

• ROUTE-ADMM demonstrated superior performance over ROUTE-BCD in computational complexity, initialization insensitivity, and recovery accuracy.
• Extensive experiments on synthetic and real data validated the efficacy of the ROUTE strategy.
• Achieved significant improvements compared to existing state-of-the-art methods.

Conclusions:

• The proposed ROUTE framework offers a robust solution for handling outliers in low-rank matrix recovery.
• ROUTE-ADMM is a highly effective and efficient approach for robust matrix recovery.
• The method shows significant potential for applications involving noisy, high-dimensional datasets.