Feature self-representation based hypergraph unsupervised feature selection via low-rank representation

Dimension reduction methods always catch many attentions, because it could effectively solve the 'curse of dimensionality' problem. In this paper, we propose an unsupervised feature selection method which could efficiently select a subset of informative features from unlabeled data. We integrate the low-rank constraint, hypergraph theory, and the self-representation property of features in a unified framework to conduct unsupervised feature selection. Specifically, we represent each feature by other features to conduct unsupervised feature selection via the feature-level self-representation property. We then embed a low-rank constraint to consider the relations among features. Moreover, a hypergarph regularizer is utilized to consider both the high-order relations and the local structure of the data. This enables the proposed model to take into account both the global structure of the data (via the low-rank constraint) and the local structure of the data (via the hypgergraph regularizer). We use an ℓ2, p-norm regularizer to satisfy the constraints. Therefore, the proposed model is more robust to the previous models due to achieving better 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 irrelevant/redundant features, compared to the state-of-the-art methods.