Multiview Subspace Clustering With Multilevel Representations and Adversarial Regularization

Multiview subspace clustering has turned into a promising technique due to its encouraging ability to discover the underlying subspace structure. In recent studies, a lot of subspace clustering methods have been developed to strengthen the clustering performance of multiview data, but these methods rarely consider simultaneously the nonlinear structure and multilevel representation (MLR) information in multiview data as well as the data distribution of latent representation. To address these problems, we develop a new Multiview Subspace Clustering with MLRs and Adversarial Regularization (MvSC-MRAR), where multiple deep auto-encoders are utilized to model nonlinear structure information of multiview data, multiple self-expressive layers are introduced into each deep auto-encoder to extract multilevel latent representations of each view data, and diversity regularizations are designed to preserve complementary information contained in different layers and different views. Furthermore, a universal discriminator based on adversarial training is developed to enforce the output of each encoder to obey a given prior distribution, so that the affinity matrix for spectral clustering (SPC) is more realistic. Comprehensive empirical evaluation with nine real-world multiview datasets indicates that our proposed MvSC-MRAR achieves significant improvements than several state-of-the-art methods in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

I. Introduction

Subspace clustering [1] is devoted to dividing a group of data samples lying in a union of multiple low-dimensional subspaces into different clusters so that the samples in the same cluster come from one subspace. With the rapid growth of various data, subspace clustering has played an increasingly vital role in pattern recognition and data mining and also been extended to various practical fields, e.g., motion segmentation [2], face clustering [3], and movie recommendation [4]. Recently, the vast majority of approaches for solving subspace clustering problems have been developed, and most of them, such as factorization-based methods [5]–[9], higher-order model-based methods [10]–[13], and self-expressiveness-based methods [14]–[18], focus on clustering linear subspaces. They generally at first calculate the affinity of each pair of data samples in the input data to construct the affinity matrix, and then use traditional clustering methods, such as normalized cuts [19] or spectral clustering (SPC) [20], to identify the clusters from the affinity matrix, thus performance of subspace clustering largely is decided by the quality of the obtained affinity matrix. Amongst these methods, the self-expressiveness-based methods have become the most popular ones, which follow a basic assumption that each data sample can be represented as a linear weighted aggregation of other samples in the same subspace based on the “self-expressiveness” property.