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Locality Preserving Projection (LPP), as a linear version of manifold learning algorithm, has attracted considerable interests in recent years. When LPP is applied to image representation and recognition, PCA is used for dimensionality reduction first. In this paper, the theoretical foundation of why LPP can perform in such orthonormal transformed subspace is presented. Based on this theoretical framework, we prove that LPP can be directly implemented in discrete cosine transform (DCT) domain. The motivation is derived from the widely applications of DCT in JPEG and MPEG standard on the one hand, and from the initially reduction of computational cost on the other hand. Experiments demonstrate competitive performance of the proposed method.