Robust graph regularized unsupervised feature selection

Recent research indicates the critical importance of preserving local geometric structure of data in unsupervised feature selection (UFS), and the well studied graph Laplacian is usually deployed to capture this property. By using a squared l2-norm, we observe that conventional graph Laplacian is sensitive to noisy data, leading to unsatisfying data processing performance. To address this issue, we propose a unified UFS framework via feature self-representation and robust graph regularization, with the aim at reducing the sensitivity to outliers from the following two aspects: i) an l2, 1-norm is used to characterize the feature representation residual matrix; and ii) an l1-norm based graph Laplacian regularization term is adopted to preserve the local geometric structure of data. By this way, the proposed framework is able to reduce the effect of noisy data on feature selection. Furthermore, the proposed l1-norm based graph Laplacian is readily extendible, which can be easily integrated into other UFS methods and machine learning tasks with local geometrical structure of data being preserved. As demonstrated on ten challenging benchmark data sets, our algorithm significantly and consistently outperforms state-of-the-art UFS methods in the literature, suggesting the effectiveness of the proposed UFS framework.