Unsupervised Hypergraph Feature Selection with Low-Rank and Self-Representation Constraints

Unsupervised feature selection is designed to select a subset of informative features from unlabeled data to avoid the issue of ‘curse of dimensionality’ and thus achieving efficient calculation and storage. In this paper, we integrate the feature-level self-representation property, a low-rank constraint, a hypergraph regularizer, and a sparsity inducing regularizer (i.e., an \(\ell _{2,1}\)-norm regularizer) in a unified framework to conduct unsupervised feature selection. Specifically, we represent each feature by other features to rank the importance of features via the feature-level self-representation property. We then embed a low-rank constraint to consider the relations among features and a hypergarph regularizer to consider both the high-order relations and the local structure of the samples. We finally use an \(\ell _{2,1}\)-norm regularizer to result in low-sparsity to output informative features which satisfy the above constraints. The resulting feature selection model thus takes into account both the global structure of the samples (via the low-rank constraint) and the local structure of the data (via the hypergraph regularizer), rather than only considering each of them used in the previous studies. This enables the proposed model more robust than the previous models due to achieving the stable feature selection model. Experimental results on benchmark datasets showed that the proposed method effectively selected the most informative features by removing the adverse effect of redundant/nosiy features, compared to the state-of-the-art methods.