Robust multi-view clustering via quadratic matrix factorization with manifold learning.

Abstract

Multi-view clustering has attracted considerable attention due to its efficiency in handling high-dimensional data. Existing approaches based on non-negative matrix factorization can achieve dimensionality reduction and yield interpretable representations. However, these methods are often limited by the assumption of linearity and sensitive to noise, making it difficult to effectively capture complex nonlinear structures in data. To address these limitations, this paper proposes a robust multi-view clustering via quadratic matrix factorization with manifold learning. The method performs a quadratic matrix factorization on each view and decouples the linear tangent space and nonlinear normal space components by subspace constraints, which enhances the robustness of the data while fitting its nonlinear structure. Furthermore, we introduce consistency and complementarity regularization terms to effectively integrate multi-view information and derive consensus low-dimensional representations. For the formulated optimization model, we have designed an alternating optimization algorithm and conducted a theoretical analysis of its convergence properties. Experimental results on nine real-world datasets and five synthetic datasets show that the clustering performance and robustness of the method are significantly better than those of existing methods.