Consensus similarity learning based on tensor nuclear norm.

Clustering approaches based on similarity learning have achieved good results, but they still have the following problems: (1) these approaches generally learn similar expressions on the original data, thereby disregarding the nonlinear structure of the data; (2) these methods generally do not consider the consistency and high-order relevance among multi-view data; and (3) these approaches generally use the learned similarity matrix for clustering, usually not achieving the optimal effect. To resolve the above issues, we present a new approach referred to as consensus similarity learning based on tensor nuclear norm. First, to address the first problem, we map the data of each view to the Hilbert space to discover the nonlinear structure of the data. Second, to address the second problem, we introduce the tensor nuclear norm to constrain the regularization term, and then, the consistency and high-order relevance among multi-view data can be captured. Third, to address the third problem, i.e., to obtain a better clustering effect, we learn a clustering indicator matrix in the kernel space instead of a similarity matrix for clustering by using a consensus representation term. Last, we incorporate these three steps into a unified framework and design the corresponding goal function. In addition, experimental outcomes on some datasets show that our algorithm is superior to certain representative approaches. [ABSTRACT FROM AUTHOR]