l₀ -Motivated Low-Rank Sparse Subspace Clustering.

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• High-dimensional data often resides in low-dimensional subspaces.
• Subspace clustering aims to identify these underlying structures.
• Existing Low-Rank Sparse Subspace Clustering (LRSSC) methods use nuclear and l1-norms, which can over-penalize and approximate the true objective.

Purpose of the Study:

• To propose novel l0 quasi-norm-based regularizations for LRSSC.
• To address the over-penalization issue inherent in l1-norm regularizations.
• To enhance the accuracy and effectiveness of subspace clustering algorithms.

Main Methods:

• Introduced a multivariate generalization of the minimax-concave penalty (GMC-LRSSC) for l0 quasi-norm regularization.
• Developed a Schatten-0 (S0) and l0-regularized objective (S0/l0-LRSSC) approximating the proximal map using proximal average.
• Employed an alternating direction method of multipliers (ADMM) to solve the resulting nonconvex optimization problems, with proven convergence.

Main Results:

• GMC-LRSSC and S0/l0-LRSSC demonstrated superior performance in subspace clustering.
• Evaluated effectiveness on both synthetic and four real-world datasets.
• Outperformed existing state-of-the-art subspace clustering methods.

Conclusions:

• The proposed GMC-LRSSC and S0/l0-LRSSC methods offer significant improvements over traditional LRSSC techniques.
• l0 quasi-norm regularizations provide a more accurate way to model rank and sparsity constraints.
• These novel methods enhance the ability to identify global and local data structures for improved clustering accuracy.