Regularized Locality Preserving Projections with Two-Dimensional Discretized Laplacian Smoothing

摘要

A novel approach to linear dimensionality reduction is introduced that is based on Locality Preserving Projections (LPP) with a discretized Laplacian smoothing term. The choice of penalty allows us to incorporate prior information that some features may be correlated. For example, an n_1 imes n_2 image represented in the plane is intrinsically a matrix. The pixels spatially close to each other may be correlated. Even though we have n_1 imes n_2 pixels per image, this spatial correlation suggests the real number of freedom is far less. However, most of the previous methods consider an image as a vector in mathbb{R}^{n_1 imes n_2}. They do not take advantage of the spatial correlation in the image, and the pixels are considered as independent pieces of information. In this paper, we introduce a Regularized LPP model using a Laplacian penalty to constrain the coefficients to be spatially smooth. By preserving the local geometrical structure of the image space, we can obtain a linear subspace which is optimal for image representation in the sense of local isometry. Recognition, clustering and retrieval can be then performed in the image subspace. Experimental results on face representation and recognition demonstrate the effectiveness of our method.