Locality Preserving Projections

Many problems in information processing involve some form of dimensionality reduction.In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis(PCA) - a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional datalies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operatoron the manifold.