“…It has been demonstrated that the locality-based LPP can usually preserve the manifold structure in the embedding space to a certain extent, and thus is relatively e®ective on some classi¯cation tasks (e.g. face recognition 8,13 ). As a result, the \locality" idea is constantly generalized, and thus many locality-based dimensionality reduction (DR) algorithms have successively been proposed, typically including unsupervised Unsupervised Discriminant Projection (UDP) a29 and OLPP, 6 semi-supervised discriminant analysis 5,26 and supervised MFA, 24 LDE, 7 ANMM, 23 GSSGE, 30 etc.…”