High-order correlation preserved multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) has attracted considerable attention as an efficient dimensionality reduction technique. Data usually exhibit certain correlations, and in multi-view data there are more complex high-order correlations. However, some MUFS methods neglect to explore the high-order correlations. In addition, existing methods focus only on the high-order correlation between views or between samples. To tackle these shortcomings, this paper proposes a high-order correlation preserved MUFS (HCFS) method, which fully preserves both the high-order correlation between views and between samples. Specifically, HCFS embeds the energy preservation into the self-representation learning for multi-view data, which preserves the global structure while performing feature selection. Meanwhile, HCFS uses the adaptive weighting strategy to fuse the self-representation matrices of each view into a consistent graph, and constructs a hypergraph based on it to maintain the high-order correlation in the consistent information. Furthermore, the high-order correlation between views is preserved by low-rank tensor learning, and the local structure of data is preserved by using the hyper-Laplacian regularization. Extensive experimental results on eight public datasets demonstrate that the proposed method outperforms several existing state-of-the-art methods, which validates the effectiveness of the proposed method.