Multi-view clustering based on generalized low rank approximation

The core of most existing graph-based multi-view clustering methods is to learn a rigid consistent spectral embedding from multiple graphs. In practice, however, such a consistency over spectral embedding may be rigorous to limit the final clustering result, since the quality and structure of different graphs are generally different. To this end, we propose to learn a relaxed consistent spectral embedding via a generalized low rank approximation model. Particularly, the proposed model introduces an adaptively weighted system which can further improve the robustness of algorithm by assigning a specific weight for each view. For the involved objective function is non-convex and non-smooth, a Relaxed MM (Majorization-Minimization) approach is developed to solve it. And, we show that Relaxed MM can reduce the computation complexity from O(n³), required by most existing graph-based methods, to O(nc²), where c and n are the number of clusters and samples, respectively, and c≪n. Numerical experiments performed on real world data demonstrate that our algorithm generally achieves comparable or better clustering results compared to eight state-of-the-art multi-view clustering methods.