Aligned multi-view clustering for unmapped data via weighted tensor nuclear norm and adaptive graph learning

Abstract

Multi-view clustering (MVC) is a prevailing clustering method that exploits consistency and complementarity among views to achieve satisfactory performance. The premise of MVC is that the samples of each view are mapped, that is, the same sample is placed in the same position among different views. However, multi-view data collected from the real world would also be unmapped, and thus conventional MVC methods are facing challenges. To address this problem, in our paper, we propose a novel aligned multi-view clustering (A-MVC) method for unmapped data. Specifically, the Calinski–Harabasz index is first employed to find the optimal view, and then the samples in other views are aligned to the samples in the optimal view with the help of the alignment matrix so that the unmapped data are converted into mapped ones. In addition, A-MVC absorbs the advantages of conventional multi-view clustering and employs both weighted tensor nuclear norm (TNN) and graph learning algorithms, which simultaneously learn the global representation and capture the local information. Finally, we integrate the alignment algorithm with a low-rank constraint based on weighted TNN and graph constraints into a unified framework. Extensive experimental results on certain unmapped multi-view datasets show that A-MVC outperforms other state-of-the-art methods. The codes and datasets are available at https://github.com/bingly/A-MVC.