Multiview Clustering Integrating Biorthogonal Nonnegative Tensor Factorization and Anchor Graph Learning

Area of Science:

• Data Science
• Machine Learning
• Artificial Intelligence

Background:

• Clustering aims to group data samples with heterogeneous features.
• Biorthogonal nonnegative matrix factorization (Bi-ONMF) and tensor factorization (Bi-ONTF) are key techniques.
• Multiview clustering (MVC) leverages data from multiple sources.

Purpose of the Study:

• Establish a theoretical link between Bi-ONMF and Bi-ONTF under the t-product framework.
• Propose a novel Bi-ONTF model with anchor graph learning (BNTF-AGL) for enhanced multiview clustering.
• Improve the ability to capture complementary information across multiple data views.

Main Methods:

• Developed a novel BNTF-AGL model integrating sparse embedding learning for anchor point selection.
• Utilized the tensor Schatten p-norm to approximate tensor tubal rank, promoting cross-view cluster assignment consistency.
• Implemented an adaptive augmented Lagrangian method (ALM) for model optimization.

Main Results:

• The proposed BNTF-AGL model effectively selects anchor points and reduces redundant connections in multiview anchor graphs.
• The tensor Schatten p-norm successfully captures complementary information, enhancing consistency in cluster assignments across views.
• The adaptive ALM method ensures convergence to a stationary Karush-Kuhn-Tucker (KKT) point.

Conclusions:

• The BNTF-AGL model demonstrates competitive or superior clustering performance on nine real-world datasets.
• The theoretical connection between Bi-ONMF and Bi-ONTF provides a foundation for advanced tensor factorization methods.
• The integration of anchor graph learning and tensor norms offers a promising direction for multiview clustering research.