Locality Preserving Embedding

Most manifold learning based methods preserve the original neighbor relationships to pursue the discriminating power. Thus, structure information of data distribution might be neglected and destroyed in low-dimensional space in a sense. In this paper, a novel supervised method, called Locality Preserving Embedding (LPE), is proposed to feature extraction and dimensionality reduction. LPE gives a low-dimensional embedding and preserves principal structure information of the local sub-manifolds. The most significant difference from existing methods is that LPE takes the distribution directions of local neighbor data into account and preserves them in low-dimensional subspace instead of only preserving the each local sub-manifold's original neighbor relationships. Therefore, LPE optimally preserves both the local sub-manifold's original neighbor relations and the distribution direction of local neighbors to separate different sub-manifolds as far as possible. The proposed LPE is applied to face recognition on the ORL and Yale face database. The experimental results show that LPE consistently outperforms the-state-of-art linear methods such as Marginal Fisher Analysis (MFA) and Constrained Maximum Variance Mapping (CMVM).