2D-LPP: A two-dimensional extension of locality preserving projections

We consider the problem of locality preserving projections (LPP) in two-dimensional sense. Recently, LPP was proposed for dimensionality reduction, which can detect the intrinsic manifold structure of data and preserve the local information. As far as matrix data, such as images, are concerned, they are often vectorized for LPP algorithm to find the intrinsic manifold structure. While the dimension of matrix data is usually very high, LPP cannot be implemented because of the singularity of matrix. In this paper, we propose a method called two-dimensional locality preserving projections (2D-LPP) for image recognition,. which is based directly on 2D image matrices rather than 1 D vectors as conventional LPP does. From an algebraic procedure, we induce that 2D-LPP is related to two other linear projection methods, which are based directly on image matrix: 2D-PCA and 2D-LDA. 2D-PCA and 2D-LDA preserve the Euclidean structure of image space, while 2D-LPP finds an embedding that preserves local information and detects the intrinsic image manifold structure. To evaluate the performance of 2D-LPP, several experiments are conducted on the ORL face database, the Yale face database and a digit dataset. The high recognition rates and speed. show that 2D-LPP achieves better performance than 2D-PCA and 2D-LDA. Experiments even show that conducting PCA after 2D-LPP achieves higher recognition than LPP at the same dimension of feature spaces. (c) 2006 Elsevier B.V. All rights reserved.