UNSUPERVISED FEATURE SELECTION WITH HILBERT-SCHMIDT INDEPENDENCE CRITERION LASSO

In recent years, it has been witnessed that feature selection can be tackled with the Hilbert-Schmidt independence criterion (HSIC) due to its effectiveness and low computational complexity. However, most of the HSIC-based feature selection methods suffer from the following limitations. First, these methods are usually just applicable to labeled data, which is not desirable since most of data in real-world applications is unlabeled. Second, existing HSIC-based unsupervised feature selection methods only addressed the general correlation between the selected features and output values that express the underlying cluster structure, while the redundancy between different features was neglected. To address these problems, we present an unsupervised feature selection method based on the HSIC least absolute shrinkage and selection operator (HSIC Lasso), which not only has a clear statistical interpretation that minimum redundant features with maximum dependence on output values can be found in terms of the HSIC, but also enables the global optimal solution to be computed efficiently by solving a Lasso optimization problem. Based on the proposed method, a unified view of feature selection based on the HSIC Lasso is also discussed. The proposed method was demonstrated with several benchmark examples.