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Low Rank Regularization: A review.

Zhanxuan Hu1, Feiping Nie1, Rong Wang2

  • 1School of Computer Science, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, PR China; Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|November 28, 2020
PubMed
Summary
This summary is machine-generated.

Low Rank Regularization (LRR) research shows non-convex relaxations outperform convex ones for data analysis. This comprehensive survey bridges LRR theory and application, highlighting superior performance in extensive experiments.

Keywords:
Low rankOptimizationRegularization

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Area of Science:

  • Machine Learning
  • Data Analysis
  • Optimization Theory

Background:

  • Low Rank Regularization (LRR) is a successful technique in data analysis, assuming data has low or approximately low rank.
  • Despite theoretical advances and practical applications, the intersection between LRR theory and application remains underexplored.

Purpose of the Study:

  • To bridge the gap between theoretical studies and practical applications of Low Rank Regularization.
  • To provide a comprehensive survey of recent advances in LRR, focusing on rank-norm relaxation and model optimization.
  • To promote the application of non-convex relaxations in LRR models through experimental validation.

Main Methods:

  • Review and summarization of recent advances in rank-norm relaxation techniques for LRR.
  • Analysis of various relaxation functions, comparing convex and non-convex approaches.
  • Summarization and analysis of optimization algorithms used for solving relaxed LRR models.
  • Extensive experimental comparison of different relaxation functions to evaluate performance.

Main Results:

  • Non-convex relaxations can effectively alleviate the punishment bias problem inherent in convex relaxations.
  • Extensive experiments demonstrate that non-convex relaxations generally offer a significant advantage over convex relaxations in LRR.
  • Specific optimization algorithms for LRR models are analyzed for their advantages and disadvantages.

Conclusions:

  • Non-convex relaxations represent a promising direction for improving the performance of Low Rank Regularization models.
  • The findings encourage further research and application of non-convex LRR methods in various data analysis tasks.
  • This survey provides a valuable resource for understanding and applying advanced LRR techniques.