Data Representation by Joint Hypergraph Embedding and Sparse Coding


Matrix factorization, also known as MF, is a well-known unsupervised learning technique for the representation of data. It has seen extensive use in the fields of Data Mining and Machine Learning. One can impose various constraints on the factorization in order to find the desired basis, which both learns the compact representation corresponding to the basis and captures high-level semantics for the data that is given. These constraints can vary according to the application scenario that is being used. We note that almost all of the previous work on MF in Data Mining has ignored the need to find such a basis, which can carry high-order semantics in the data. This is something that we find very interesting. In this piece, we present a novel MF framework that we call Joint Hypergraph Embedding and Sparse Coding (JHESC). In this framework, the basis that is obtained captures high-order semantic information in the data. To be more specific, we first propose a new hypergraph learning model in order to obtain a more discriminative basis by hypergraph-based Laplacian Eigenmap. Next, sparse coding is performed on the learned basis in order to ensure that the new representation has a higher capacity for identification. In addition, we improve the efficacy of our approach to dealing with nonlinear data by extending the proposed method to the reproducing kernel Hilbert space. Extensive experimental results on data clustering show that the proposed method consistently outperforms the other state-of-the-art matrix factorization methods. This was demonstrated by the results of the experiments.

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