Multi-hypergraph Incidence Consistent Sparse Coding for Image Data Clustering

Abstract

Sparse representation has been a powerful technique for modeling image data and thus enhance the performance of image clustering. Sparse coding, as an unsupervised way to extract sparse representation, learns a dictionary that represents high-level semantics and the new representations on the dictionary. Though existing sparse coding schemes are considering local manifold structure of the data with graph/hypergraph regularization, more from the manifold should be exploited to utilize intrinsic manifold characteristics in the data. In this paper, we firstly propose a Hypergraph Incidence Consistency regularization term by minimizing the reconstruction error of the hypergraph incidence matrix with sparse codes to further regulate the learned sparse codes with hypergraph-based manifold. Moreover, a multi-hypergraph learning framework to automatically select the optimal manifold structure is integrated into the objective of sparse coding learning, resulting in multi-hypergraph incidence Consistent Sparse Coding (MultiCSC). We show that the MultiCSC objective function can be optimized efficiently, and that several existing sparse coding methods are special cases of MultiCSC. Extensive experimental results on image clustering demonstrate the effectiveness of our proposed method.