Multi-Hypergraph Consistent Sparse Coding

Sparse representation has been a powerful technique for modeling high-dimensional data. As an unsupervised technique to extract sparse representations, sparse coding encodes the original data into a new sparse code space and simultaneously learns a dictionary representing high-level semantics. Existing methods have considered local manifold within high-dimensional data using graph/hypergraph Laplacian regularization, and more from the manifold could be utilized to improve the performance. In this article, we propose to further regulate the sparse coding so that the learned sparse codes can well reconstruct the hypergraph structure. In particular, we add a novel hypergraph consistency regularization term (HC) by minimizing the reconstruction error of the hypergraph incidence or weight matrix. Moreover, we extend the HC term to multi-hypergraph consistent sparse coding (MultiCSC) and automatically select the optimal manifold structure under the multi-hypergraph learning framework. We show that the optimization of MultiCSC can be solved efficiently, and that several existing sparse coding methods can fit into the general framework of MultiCSC as special cases. As a case study, hypergraph incidence consistent sparse coding is applied to perform semi-auto image tagging, demonstrating the effectiveness of hypergraph consistency regulation. We perform further experiments using MultiCSC for image clustering, which outperforms a number of baselines.

Authors

• Xiaodong Feng
• Sen Wu Harbin Institute of Technology, Shenzhen
• Wenjun Zhou

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