Multi-graph fusion guided robust adaptive learning for subspace clustering

Abstract

Subspace clustering is an advanced technique that identifies clusters embedded within a union of low-dimensional subspaces of the original data space, thereby revealing its intrinsic structure. Spectral clustering-based methods have gained significant attention in computer vision, image processing and pattern recognition due to their promising performance. However, existing approaches, which typically rely on self-representation for representation coefficient learning, often lack robustness and struggle to comprehensively characterize complex data structures. Traditional reconstruction loss based on the Frobenius or ${\ell }_1$ norm are susceptible to noise and outliers. Furthermore, many methods underutilize inherent data characteristics for capturing local geometric structures and adapting to intricate data relationships. To address these limitations, this paper proposes a novel subspace clustering approach, named Multi-graph Fusion Guided Robust Adaptive Learning (MFGRAL), which integrates robust adaptive representation and multi-graph fusion within a unified framework. Specifically, a non-convex logarithmic loss function is adopted to enhance robustness against noise and outliers. To better preserve local manifold structures, a multi-graph fusion strategy is developed to guide the adaptive graph learning process. This facilitates the learning of more discriminative low-dimensional embeddings and enhances the capacity to capture complex neighborhood relationships. An effective and efficient optimization algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed to solve the proposed model. Extensive experimental results on several benchmark datasets demonstrate the effectiveness of the proposed MFGRAL and its superiority over state-of-the-art methods.