Interpretable nonconvex submodule clustering algorithm using ℓr-induced tensor nuclear norm and ℓ2,p column sparse...

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Tensor-based subspace clustering excels with high-dimensional data.
• Traditional methods struggle with 2D image data due to vectorization losing higher-order correlations.

Purpose of the Study:

• To propose a novel non-convex submodule clustering approach (2D-NLRSC) for 2D image data.
• To overcome limitations of vectorization in preserving tensor correlations for image clustering.

Main Methods:

• Developed 2D-NLRSC leveraging sparse and low-rank representations for 2D image data.
• Introduced an [Formula: see text]-induced tensor nuclear norm for precise tensor rank approximation.
• Arranged samples as lateral slices of a third-order tensor, utilizing t-product for low-rank representation.

Main Results:

• The proposed method combines [Formula: see text]-norm clustering awareness with Laplacian regularization for a diagonal structure representation tensor.
• Incorporated the [Formula: see text]-norm for regularization, benefiting from its invariance, continuity, and differentiability.
• Experimental results on real image datasets demonstrated the superior performance of the 2D-NLRSC model.

Conclusions:

• 2D-NLRSC effectively addresses the challenge of preserving higher-order tensor correlations in 2D image clustering.
• The novel approach achieves superior performance compared to existing methods on real-world image datasets.