Abstract: The traditional linear regression method used for data dimensionality reduction failed to capture the geometry structure of data. In order to solve this problem, we present a local structure preserving based data dimensionality reduction. A nonnegative least squares method is introduced to construct the graph, which describe the local neighborhood geometry structure information. For the integrating of global structural information and local structure information integration, we also introduce a new model selection method for model parameter estimation, greatly reducing the cost of computation. Experiments on five benchmark datasets(ORL, YaleB, USPS, 20Newgroup and Isolet)show that the proposed approach can achieve better results than ULDA, OLDA and NPE.