Logarithmic Schatten- p Norm Minimization for Tensorial Multi-View Subspace Clustering.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Low-rank tensor decomposition is crucial for multi-view clustering, capturing high-order correlations.
• Current Tensor Nuclear Norm (TNN) methods over-penalize singular values, limiting representation accuracy.
• A more effective tensor rank surrogate is needed for improved multi-view analysis.

Purpose of the Study:

• To propose a novel tensor logarithmic Schatten-p norm (pNM) as a superior surrogate for tensor rank.
• To develop a pNM minimization-based multi-view subspace clustering (pNM-MSC) model.
• To enhance the characterization of high-order correlations and complementary information in multi-view data.

Main Methods:

• A new penalty function, the tensor logarithmic Schatten-p norm (pNM), is introduced to better approximate tensor rank.
• A pNM minimization-based multi-view subspace clustering (pNM-MSC) model is formulated.
• The Alternating Direction Method of Multipliers (ADMM) is employed to solve the non-convex optimization problem, with convergence analysis provided.

Main Results:

• The proposed pNM effectively preserves significant singular values while discarding redundant ones.
• The pNM-MSC model demonstrates superior performance across nine benchmark datasets compared to existing methods.
• The method accurately captures high-order correlations and complementary information among multiple views.

Conclusions:

• The tensor logarithmic Schatten-p norm offers a more effective approach to low-rank tensor approximation.
• The pNM-MSC model significantly advances multi-view subspace clustering performance.
• This work provides a robust and convergent algorithm for analyzing complex multi-view data.