Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Multi-view clustering (MVC) algorithms group samples across datasets but face scalability and robustness issues.
• Existing methods struggle with computational overhead, noise, and feature redundancy in high-dimensional data.
• Nonnegative matrix factorization (NMF) methods offer scalability but have limitations in shared coefficient matrix assumptions.

Purpose of the Study:

• To propose a novel tensorized multi-dimensional multi-view clustering (TMMVC) method based on NMF.
• To address limitations of existing MVC algorithms, including computational cost, noise, and feature redundancy.
• To enhance clustering accuracy and robustness for large-scale, high-dimensional multi-view data.

Main Methods:

• Mapping each view into embedding spaces of different dimensionalities using NMF to obtain view-specific basis matrices.
• Aligning and fusing coefficient matrices into a unified consensus representation via view-specific rotation matrices in a shared subspace.
• Forming a third-order tensor from the fused representation and feature mapping, regularized by a tensor Schatten-p norm.
• Utilizing the Augmented Lagrange Multiplier (ALM) method for optimization.

Main Results:

• The proposed TMMVC method significantly reduces computational overhead.
• Tensor Schatten-p norm regularization enhances the capture of underlying global structure.
• Experimental results demonstrate consistent outperformance of TMMVC over state-of-the-art MVC algorithms.
• TMMVC shows superior clustering accuracy and scalability on benchmark datasets.

Conclusions:

• TMMVC effectively addresses the limitations of existing multi-view clustering methods.
• The tensorization approach enhances robustness and accuracy in high-dimensional data.
• TMMVC offers a scalable and effective solution for large-scale multi-view clustering tasks.