Global and intrinsic geometric structure embedding for unsupervised feature selection

Dimensionality reduction becomes a significant problem due to the proliferation of high dimensional data. Sparse preserving projection (SPP) obtains the intrinsic geometric structure of the data, which contains natural discriminating information, and avoids the selection of parameters as well. However, SPP neglects the global structures since it computes the sparse representation of each data individually. Low rank representation (LRR), another commonly used dimensionality reduction method, finds the lowest rank representation of all data jointly, and is capable of capturing the global structures of data. Therefore in this paper, we propose a method, global and intrinsic geometric structure embedding for unsupervised feature selection (GGEFS), by constructing a low-rank-sparse graph. Our GGEFS method contains the loss of information, the preservation of structural information and the sparse regularization of projection matrix, on which we impose l2,1/2-matrix norm to select sparser and discriminative features. An effective iterative algorithm based on Lagrange Multiplier method is described to solve GGEFS. Extensive experimental results demonstrate that the proposed algorithm outperform several state-of-the-art unsupervised feature selection methods.