The　objective　of　self-expression　based　spectral　clustering　is　to　learn　an　affinity　matrix　which　accurately　reflects　the　similarity　among　data,　and　the　Laplacian　constraint　is　usually　exploited　to　make　the　affinity　matrix　preserve　the　global　structure　of　raw　data.　However,　there　exist　two　drawbacks:　firstly,　these　methods　are　mostly　designed　for　vectorial　data　in　Euclidean　spaces,　which　are　not　suitable　for　multidimensional　data　with　nonlinear　manifold　structure,　e.g.,　videos　and　image-sets.　Secondly,　the　clustering　performance　heavily　relies　on　the　quality　of　a　pre-learned　Laplacian　matrix　in　which　the　global　structure　may　be　mis-interpreted　without　considering　manifold　structures.　In　this　paper,　we　firstly　provide　a　unified　framework　about　self-expression　learning　on　Grassmann　manifolds,　which　implements　the　clustering　tasks　for　multidimensional　data　under　subspace　views.　Then,　to　assign　optimal　neighbors　to　each　data　depending　on　the　local　distance,　we　adaptively　learn　the　neighborhood　relationship　from　the　obtained　self-expression　coefficient　matrix,　referred　to　Learning　Adaptive　Neighborhood　Graph　on　Grassmann　manifolds　(GMAN).　In　the　optimization　process,　the　neighborhood　relationship　can　be　adaptively　learned　and　updated　with　the　coefficient　matrix.　The　experimental　results　on　five　public　datasets　show　that　the　proposed　method　is　obviously　better　than　many　related　clustering　methods　based　on　Grassmann　manifolds,　proving　the　effectiveness　of　GMAN　in　multidimensional　data　clustering.　©　1999-2012　IEEE.