Abstract: This paper proposes a new approach to perform the discriminant analysis on the labelled high dimensional image data with intra-class sub-manifolds. Real world images are usually taken from the different camera views. Pose, illumination, glasses and gender of the persons taking the facial images usually lead to multi-modality or high curvature of the underlying manifold structures. These variations result in the degraded performance of many existing algorithms. This paper proposes to preserve the within-class local structure, while imposing constrain on the variances only in the directions normal to the between-class margin. The experiments on Yale-B and UMIST face database show that the proposed algorithm outperforms many approaches such as LPP (locality preserving projections) and FDA (fisher discriminant analysis).