Learning from normalized local and global discriminative information for semi-supervised regression and dimensionality reduction

Semi-supervised dimensionality reduction is one of the important topics in pattern recognition and machine learning. During the past decade, Laplacian Regularized Least Square (LapRLS) and Semi-supervised Discriminant Analysis (SDA) are the two widely-used semi-supervised dimensionality reduction methods. In this paper, we show that SDA and LapRLS can be unified into a constrained manifold regularized least square framework. The manifold term, however, cannot fully utilize the underlying discriminative information. We thus introduce a new and effective semi-supervised dimensionality reduction method, called Learning from Local and Global Information (LLGDI), to solve the problem. The proposed LLGDI method adopts a set of local classification functions to preserve both local geometrical and discriminative information of dataset. It also adopts a global classification function to preserve the global discriminative information, and an uncorrelated constraint to calculate the projection matrix for simultaneously solving regression and dimensionality reduction problem. As a result, the LLGDI method is able to preserve local discriminative, manifold information as well as the global discriminative information. Theoretical analysis and extensive simulations presented in the paper show the effectiveness of the LLGDI algorithm. The results also demonstrate LLGDI can achieve superior performance compared with other existing methods.