Local Discriminant Space Alignment

Dimensionality reduction has been demonstrated to be an effective way for feature extraction in the pattern recognition task. In this paper, a new manifold learning algorithm, Local Discriminant Space Alignment (LDSA), is developed for nonlinear dimensionality reduction. In LDSA, the discriminant structure and the local geometry of data manifold is learned by constructing a local space for each data point through local discriminant analysis, and those discriminant subspaces are aligned to give the internal global coordinates of data points with respect to the underlying manifold. To solve the out of sample problem, the linearization of LDSA (LLDSA) is also proposed and is applied to face recognition. The Experimental results on ORL and Yale database showed the effectiveness of LLDSA in comparison with existing dimensionality reduction algorithms designed for feature extraction.