Nonnegative　Matrix　Factorization　(NMF),　as　a　popular　feature　extraction　technique,　has　recently　attracted　increasing　attentions　in　high-dimensional　data　analysis,　due　to　the　strong　ability　of　dimension　reduction　and　semantic　representation.　In　order　to　utilize　the　partial　label　information　in　practice,　several　semi-supervised　NMF　methods　have　been　proposed.　However,　existing　semi-supervised　NMF　variants　only　consider　the　global　label　constraint　of　data,　but　ignore　the　local　label　information　embedded　in　geometric　structure,　which　is　very　crucial　for　data　representation.　To　address　the　above　issue,　we　propose　an　improved　NMF　method,　namely　local　and　global　regularized　semi-supervised　NMF　(LGNMF),　by　considering　the　local　and　global　label　constraints　simultaneously.　Specifically,　the　local　label　constraint　is　depicted　in　a　graph,　which　is　pre-computed　by　metric　learning.　In　addition,　to　explore　the　global　label　information,　we　construct　an　indicator　matrix　to　restrict　the　coefficient　matrix　in　LGNMF.　For　the　formulated　LGNMF,　a　multiplicative　update　rule　(MUR)　is　developed.　Extensive　experiments　on　several　real　datasets　demonstrate　the　superiority　of　the　proposed　method　over　the　state-of-the-art　methods　in　terms　of　clustering　accuracy　and　normalized　mutual　information.　©　2019　IEEE.