The embedding proximity learning for multi-view clustering

Most cutting-edge multi-view clustering techniques typically focus on extracting consistent structural features from similarity matrices. However, these methods only consider clustering in the same potential space, which has led to interference from high-dimensional noise and limits semantic information mining. In addition, the method of generating the graph also has an important influence on the clustering result. To address these problems, we introduce a novel embedding proximity learning method for multi-view clustering (EPLMC). Specifically, EPLMC refines and processes similarity matrices derived from each view, reconstructing them to form a cohesive and unified embedding on the Grassmann manifold, which enhances the extraction of semantic information while mitigating the disruptive effects of high-dimensional noise. This uniform embedding consequently improves the representation of data similarity matrices across multiple views, achieving the dynamic construction of similarity matrices. To emphasize the differences among views, we introduce a self-weighted framework. The essence of EPLMC lies in its innovative learning methodology, which facilitates the simultaneous learning of similarity matrices and the unified embedding in a mutually reinforcing way. To tackle the optimization challenge posed by EPLMC, we introduce a highly efficient iterative algorithm, accompanied by an in-depth analysis of both its convergence properties and computational complexity. Extensive empirical results convincingly demonstrate EPLMC's superiority over ten state-of-the-art methods across nine real-world datasets.