Semisupervised　learning　is　an　effective　technique　to　represent　the　intrinsic　features　of　a　hyperspectral　image　(HSI),　which　can　reduce　the　cost　to　obtain　the　labeled　information　of　samples.　However,　traditional　semisupervised　learning　methods　fail　to　consider　multiple　properties　of　an　HSI,　which　has　restricted　the　discriminant　performance　of　feature　representation.　In　this　article,　we　introduce　the　hypergraph　into　semisupervised　learning　to　reveal　the　complex　multistructures　of　an　HSI,　and　construct　a　semisupervised　discriminant　hypergraph　learning　(SSDHL)　method　by　designing　an　intraclass　hypergraph　and　an　interclass　graph　with　the　labeled　samples.　SSDHL　constructs　an　unsupervised　hypergraph　with　the　unlabeled　samples.　In　addition,　a　total　scatter　matrix　is　used　to　measure　the　distribution　of　the　labeled　and　unlabeled　samples.　Then,　a　low-dimensional　projection　function　is　constructed　to　compact　the　properties　of　the　intraclass　hypergraph　and　the　unsupervised　hypergraph,　and　simultaneously　separate　the　characteristics　of　the　interclass　graph　and　the　total　scatter　matrix.　Finally,　according　to　the　objective　function,　we　can　obtain　the　projection　matrix　and　the　low-dimensional　features.　Experiments　on　three　HSI　data　sets　(Botswana,　KSC,　and　PaviaU)　show　that　the　proposed　method　can　achieve　better　classification　results　compared　with　a　few　state-of-the-art　methods.　The　result　indicates　that　SSDHL　can　simultaneously　utilize　the　labeled　and　unlabeled　samples　to　represent　the　homogeneous　properties　and　restrain　the　heterogeneous　characteristics　of　an　HSI.　©　2008-2012　IEEE.