Abstract

In recent years, hypergraph modeling has shown its superiority on correlation formulation among samples and has wide applications in classification, retrieval, and other tasks. In all these works, the performance of hypergraph learning highly depends on the generated hypergraph structure. A good hypergraph structure can represent the data correlation better, and vice versa. Although hypergraph learning has attracted much attention recently, most of existing works still rely on a static hypergraph structure, and little effort concentrates on optimizing the hypergraph structure during the learning process. To tackle this problem, we propose the first dynamic hypergraph structure learning method in this paper. In this method, given the originally generated hypergraph structure, the objective of our work is to simultaneously optimize the label projection matrix (the common task in hypergraph learning) and the hypergraph structure itself. On one hand, the label projection matrix is related to the hypergraph structure in our formulation, similar to traditional methods. On the other hand, different from the existing hypergraph generation methods based on the feature space only, the hypergraph structure optimization in our formulation utilizes the data correlation from both the label space and the feature space. Then, we alternatively learn the optimal label projection matrix and the hypergraph structure, leading to a dynamic hypergraph structure during the learning process. We have applied the proposed method in the tasks of 3D shape recognition and gesture recognition. Experimental results on four public datasets show better performance compared with the state-of-the-art methods. We note that the proposed method can be further applied in other tasks.

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