Hyperspectral　image　(HSI)　contains　complex　multiple　structures.　Therefore,　the　key　problem　analyzing　the　intrinsic　properties　of　an　HSI　is　how　to　represent　the　structure　relationships　of　the　HSI　effectively.　Hypergraph　is　very　effective　to　describe　the　intrinsic　relationships　of　the　HSI.　In　general,　Euclidean　distance　is　adopted　to　construct　the　hypergraph.　However,　this　method　cannot　effectively　represent　the　structure　properties　of　high-dimensional　data.　To　address　this　problem,　we　propose　a　sparse-adaptive　hypergraph　discriminant　analysis　(SAHDA)　method　to　obtain　the　embedding　features　of　the　HSI　in　this　letter.　SAHDA　uses　the　sparse　representation　to　reveal　the　structure　relationships　of　the　HSI　adaptively.　Then,　an　adaptive　hypergraph　is　constructed　by　using　the　intraclass　sparse　coefficients.　Finally,　we　develop　an　adaptive　dimensionality　reduction　mode　to　calculate　the　weights　of　the　hyperedges　and　the　projection　matrix.　SAHDA　can　adaptively　reveal　the　intrinsic　properties　of　the　HSI　and　enhance　the　performance　of　the　embedding　features.　Some　experiments　on　the　Washington　DC　Mall　hyperspectral　data　set　demonstrate　the　effectiveness　of　the　proposed　SAHDA　method,　and　SAHDA　achieves　better　classification　accuracies　than　the　traditional　graph　learning　methods.　©　2019　IEEE.