One-step Multi-view Clustering with Consensus Graph and Data Representation Convolution

Multi-view clustering aims to partition unlabeled patterns into disjoint clusters using consistent and complementary information derived from features of patterns in multiple views. Downstream methods perform this clustering sequentially: estimation of individual or consistent similarity matrices, spectral embedding, and clustering. In this article, we present an approach that can address some of the shortcomings of previous multiview clustering methods. We propose a single objective function whose optimization can jointly provide the consistent graph matrix for all views, the unified spectral data representation, the cluster assignments, and the view weights. We propose a new constraint term that sets the cluster index matrix to the convolution of the consistent spectral projection matrix over the consistent graph. Our proposed scheme has two interesting properties that the recent works do not have simultaneously. First, the cluster assignments can be estimated directly without the need for an additional clustering phase, which depends heavily on initialization. Second, the soft cluster assignments are directly linked to the kernel representation of the features of the views. Moreover, our method automatically computes the weights of each view, requiring fewer hyperparameters. We have conducted a series of experiments on real datasets. These demonstrate the effectiveness of the proposed approach, which compares favorably to many competing multi-view clustering methods.