Dimensionality　reduction　is　a　key　technology　for　face　recognition.　In　this　paper,　we　propose　a　novel　method,　called　Locality　Preserving　Fisher　Discriminant　Analysis　(LPFDA),　which　extends　the　original　Fisher　Discriminant　Analysis　by　preserving　the　locality　structure　of　the　data.　LPFDA　can　get　a　sub-space　projection　matrix　by　solving　a　generalized　eigenvalue　problem.　Several　experiments　are　conducted　to　demonstrate　the　effectiveness　and　robustness　of　our　method.