Unsupervised Feature Selection via Multi-Structure Learning and Indicator Matrix

Traditional feature selection methods usually only consider a specific geometric structure of the original data, which cannot reveal the most essential underlying structure of the data. Apart from this, a regularization constraint with sparsity is often imposed on the mapping matrix, which inevitably leads to additional parameter setting issues. To address these challenges, a novel unsupervised feature selection via multi-structure learning and indicator matrix (UFSMI) is proposed in this study. More concretely, we construct a unified framework that incorporates multi-structure learning and feature selection. UFSMI first explores the global and local geometric structure of high dimensional data in subspace to excavate the intrinsic structure of data, effectively reducing the interference of redundant features. Then, an indicator matrix for feature selection that can explicitly indicate which features should be selected is in-troduced without imposing any regularization constraints. Finally, the most useful subset of features can be obtained based on the indices of the non-zero elements in the indicator matrix. A series of experiments are conducted to demonstrate the effectiveness and superiority of the proposed method on nine real-word high dimensional datasets by comparing with existing state-of-the-art feature selection methods.