Locality Preserving Embedding
Zhihui Lai, Minghua Wan, Zhong Jin · 2009
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).