Asymptotics-Aware Multi-View Subspace Clustering

Abstract

Recently, multi-view subspace clustering has attracted extensive attention due to the rapid increase of multi-view data in many real-world applications. The main goal of this task is to learn a common representation of multiple subspaces from the given multi-view data, and most existing methods usually directly merge multiple groups of features by the single-step integration. However, there may exist large disparities among different views of the data, and thus the conventional single-step practice can hardly obtain a generally consistent feature representation for the multi-view data. To overcome this challenge, we present a novel approach dubbed “Asymptotics-Aware Multi-view Subspace Clustering (A$^{2}$MSC)” to pursue a consistent feature representation in a multi-step way, which iteratively conducts the data recovery to gradually reduce the differences between pairwise views. Specifically, we construct an asymptotic learning rule to update the feature representation, and the iteration result converges to a consistent feature vector for characterizing each instance of the original multi-view data. After that, we utilize such a new feature representation to learn a clustering-oriented similarity matrix via minimizing a self-expressive objective, and we also design the corresponding optimization algorithm to solve it with convergence guarantees. Theoretically, we prove that the learned asymptotic representation effectively integrates multiple views, thereby ensuring the effective handling of multi-view data. Empirically, extensive experimental results demonstrate the superiority of our proposed A$^{2}$MSC over the state-of-the-art multi-view subspace clustering approaches.