Two-dimensional complete neighborhood preserving embedding

Complete neighborhood preserving embedding (CNPE) is an improvement to the neighborhood preserving embedding (NPE) algorithm, which can address the singularity and stability problems of NPE and at the same time preserve useful discriminative information. However, CNPE works with vectorized representations of data, and thus, the original 2D face image matrices should be previously transformed into the same dimensional vectors. Such a matrix-to-vector transform usually leads to a high-dimensional image vector space, which makes the eigenanalysis quite difficult and time-consuming. Beyond computational issues, some spatial structural information between nearby pixels may be lost after vectorization. In this paper, we develop a new scheme for image feature extraction, namely, two-dimensional complete neighborhood preserving embedding (2D-CNPE). 2D-CNPE builds the eigenmatrix and the weight matrix which characterize local neighborhood properties of data directly based on the original face images, and then, the optimal embedding axes are obtained by performing an eigen-decomposition. Experimental results on three face databases show that the proposed 2D-CNPE achieves better performance than other feature extraction methods, such as Eigenfaces, Fisherfaces, and 2D-PCA.