Robust energy preserving embedding for multi-view subspace clustering

With the increasing popularity of multi-view data, multi-view subspace clustering (MVSC) has attracted intensive attention. However, the curse of dimensionality of the high-dimensional multi-view data constantly obsesses the development of multi-view method. Together with the curse of dimensionality, the existence of noise and outliers further obstructs the ability of MVSC to exploit the underlying subspace structure. To solve these challenging problems, in this paper, we propose a novel MVSC method, namely robust energy preserving embedding (REPE), which aims to exploit the underlying subspace structure of multi-view data through energy preserving embedding projection and low-rank constraint. In a different manner than before, we use dictionary learning to integrate self-expressiveness learning and embedded subspace learning together, ensure the preservation of energy by restoring the data in embedding space to the original space. Moreover, Schatten p-norm is introduced to better approximate the low-rank constraint. So that we can reduce the dimension of the data while maintain the major energy of the original view data. Thereby, a high quality affinity graph can be learned, such that the promising clustering results can subsequently be obtained. Extensive experiments on five benchmarks have validated the effectiveness of the proposed method, by comparing it with the state of arts.