Robust Multi-View Clustering via Quadratic Matrix Factorization With Manifold Learning.

Area of Science:

• Data Science
• Machine Learning
• Pattern Recognition

Background:

• Multi-view clustering is effective for high-dimensional data.
• Non-negative matrix factorization (NMF) methods offer dimensionality reduction but struggle with nonlinearity and noise.
• Existing NMF-based approaches fail to capture complex nonlinear structures.

Purpose of the Study:

• To propose a robust multi-view clustering method addressing limitations of linear NMF.
• To enhance data robustness and fit nonlinear structures using quadratic matrix factorization.
• To integrate multi-view information for consensus low-dimensional representations.

Main Methods:

• Quadratic matrix factorization applied to each data view.
• Decoupling linear tangent and nonlinear normal space components via subspace constraints.
• Consistency and complementarity regularization terms for multi-view integration.
• Alternating optimization algorithm with convergence analysis.

Main Results:

• The proposed method effectively captures complex nonlinear data structures.
• Enhanced robustness against noise compared to traditional methods.
• Experimental validation on diverse real-world and synthetic datasets.
• Demonstrated superior clustering performance and robustness over existing techniques.

Conclusions:

• The quadratic matrix factorization with manifold learning offers a robust solution for multi-view clustering.
• The method successfully handles nonlinearities and integrates multi-view information.
• It provides a significant advancement over existing linear NMF-based approaches.