In this paper, we propose an unsupervised feature selection framework which simultaneously preserves the local geometric structure and global discriminative structure of data. Also, the spectral clustering algorithm is incorporated into this framework to exploit the discriminative structure. To demonstrate the generality of our framework, we instantiate our framework into two specific algorithms by characterizing the local geometric structure of data with two well-known models, i.e., locally linear embedding and linear preserve projection. After that, we provide an efficient algorithm with proved convergence to solve the resultant optimization problem. Comprehensive experiments have been conducted on eleven benchmark data sets and the results demonstrate the superior performance of our framework.