Global Discriminant Analysis for Unsupervised Feature Selection with Local Structure Preservation

Feature selection is an efficient technique for data dimension reduction in data mining and machine learning. Unsupervised feature selection is much more difficult than supervised feature selection due to the lack of label information. Discriminant analysis is powerful to select discriminative features, while local structure preservation is important to unsupervised feature selection. In this paper, we incorporate discriminant analysis, local structure preservation and l2,1-norm regularization into a joint framework for unsupervised feature selection. The global structure of data is captured by the discriminant analysis, while the local manifold structure is revealed by the locality preserving projections. By imposing row sparsity on the transformation matrix, the resultant formulation optimizes for selecting the most discriminative features which can better capture both the global and local structure of data. We develop an efficient algorithm to solve the l2,1-norm-based optimization problem in our method. Experimental results on different types of real-world data demonstrate the effectiveness of the proposed method.