Locality Preserving Projections (LPP) were proposed by He and Niyoigi in 2003. LPP are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP can be seen as an alternative to PCA.. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, LPP are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold.