Locality　preserving　projection　(LPP)　is　a　widely　used　linear　dimensionality　reduction　method,　which　preserves　the　locality　structure　of　the　original　data.　Motivated　by　the　fact　that　kernel　technique　can　capture　nonlinear　similarity　of　features　and　help　to　improve　separability　between　nearby　data　points,　this　paper　proposes　locality　preserving　projection　model　based　on　Euler　representation　(named　as　ELPP).　This　model　first　projects　the　data　into　a　complex　space　with　Euler　representation,　then　learns　the　dimensionality　reduction　projection　with　preserving　locality　structure　in　this　complex　space.　We　also　extend　ELPP　to　F-ELPP　by　replacing　the　squared　F-norm　with　F-norm,　which　will　weaken　the　exaggerated　errors　and　be　more　robustness　to　outliers.　The　optimization　algorithms　of　the　two　models　are　given,　and　the　convergence　of　F-ELPP　is　proved.　A　large　number　of　experiments　on　several　public　databases　have　demonstrated　that　the　two　proposed　models　have　good　robustness　and　feature　extraction　ability.　(C)　2020　Elsevier　Inc.　All　rights　reserved.