Learning a Spatially Smooth Subspace for Face Recognition

Abstract

Subspace learning based face recognition methods have attracted considerable interests in recently years, including principal component analysis (PCA), linear discriminant analysis (LDA), locality preserving projection (LPP), neighborhood preserving embedding (NPE), marginal fisher analysis (MFA) and local discriminant embedding (LDE). These methods consider an n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> timesn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> image as a vector in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">timesn</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and the pixels of each image are considered as independent. While an image represented in the plane is intrinsically a matrix. The pixels spatially close to each other may be correlated. Even though we have n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> xn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> pixels per image, this spatial correlation suggests the real number of freedom is far less. In this paper, we introduce a regularized subspace learning model using a Laplacian penalty to constrain the coefficients to be spatially smooth. All these existing subspace learning algorithms can fit into this model and produce a spatially smooth subspace which is better for image representation than their original version. Recognition, clustering and retrieval can be then performed in the image subspace. Experimental results on face recognition demonstrate the effectiveness of our method.