Locality　preserving　projection　(LPP)　is　a　well-known　method　for　dimensionality　reduction　in　which　the　neighborhood　graph　structure　of　data　is　preserved.　Traditional　LPP　employ　squared　F-norm　for　distance　measurement.　This　may　exaggerate　more　distance　errors,　and　result　in　a　model　being　sensitive　to　outliers.　In　order　to　deal　with　this　issue,　we　propose　two　novel　F-norm-based　models,　termed　as　F-LPP　and　F-2DLPP,　which　are　developed　for　vector-based　and　matrix-based　data,　respectively.　In　F-LPP　and　F-2DLPP,　the　distance　of　data　projected　to　a　low　dimensional　space　is　measured　by　F-norm.　Thus　it　is　anticipated　that　both　methods　can　reduce　the　influence　of　outliers.　To　solve　the　F-norm-based　models,　we　propose　an　iterative　optimization　algorithm,　and　give　the　convergence　analysis　of　algorithm.　The　experimental　results　on　three　public　databases　have　demonstrated　the　effectiveness　of　our　proposed　methods.　Copyright　©　2018,　Association　for　the　Advancement　of　Artificial　Intelligence　(www.aaai.org).　All　rights　reserved.