LRR for Subspace Segmentation via Tractable Schatten-$p$ Norm Minimization and Factorization.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Nuclear norm-based Low Rank Representation (LRR) is widely used for tasks like subspace segmentation.
• Existing nuclear norm methods suffer from suboptimal solutions and high computational cost due to singular value decomposition.

Purpose of the Study:

• To develop more accurate and efficient LRR variants by overcoming the limitations of nuclear norm-based methods.
• To introduce Schatten-p norm minimization (SpNM_LRR) and Schatten-p norm factorization (SpNFLRR) for LRR.

Main Methods:

• Proposed two tractable variants of LRR: SpNM_LRR and SpNFLRR, using Schatten-p norms for p=1, 2/3, and 1/2.
• Employed a multi-block alternating direction method of multipliers (ADMM) with auxiliary variables to solve the proposed LRR variants.
• Analyzed the computational complexity and convergence properties of the nonconvex multi-block ADMM algorithms.

Main Results:

• The proposed SpNM_LRR and SpNFLRR methods demonstrate improved accuracy compared to traditional nuclear norm-based LRR.
• Experimental results on synthetic and real-world data confirm the efficacy and efficiency of the developed methods.
• The ADMM-based approach effectively handles the nonconvex optimization problems associated with Schatten-p norms.

Conclusions:

• Schatten-p norm-based LRR variants offer a more effective and computationally efficient alternative to nuclear norm-based LRR.
• The proposed ADMM framework provides a robust solution for solving these nonconvex LRR problems.
• The validated methods show significant potential for applications requiring accurate and fast subspace segmentation.