Clustering　is　one　of　the　fundamental　topics　in　data　mining　and　pattern　recognition.　As　a　prospective　clustering　method,　the　subspace　clustering　has　made　considerable　progress　in　recent　researches,　e.g.,　sparse　subspace　clustering　(SSC)　and　low　rank　representation　(LRR).　However,　most　existing　subspace　clustering　algorithms　are　designed　for　vectorial　data　from　linear　spaces,　thus　not　suitable　for　high-dimensional　data　with　intrinsic　non-linear　manifold　structure.　For　high-dimensional　or　manifold　data,　few　research　pays　attention　to　clustering　problems.　The　purpose　of　clustering　on　manifolds　tends　to　cluster　manifold-valued　data　into　several　groups　according　to　the　mainfold-based　similarity　metric.　This　article　proposes　an　extended　LRR　model　for　manifold-valued　Grassmann　data　that　incorporates　prior　knowledge　by　minimizing　partial　sum　of　singular　values　instead　of　the　nuclear　norm,　namely　Partial　Sum　minimization　of　Singular　Values　Representation　(GPSSVR).　The　new　model　not　only　enforces　the　global　structure　of　data　in　low　rank,　but　also　retains　important　information　by　minimizing　only　smaller　singular　values.　To　further　maintain　the　local　structures　among　Grassmann　points,　we　also　integrate　the　Laplacian　penalty　with　GPSSVR.　The　proposed　model　and　algorithms　are　assessed　on　a　public　human　face　dataset,　some　widely　used　human　action　video　datasets　and　a　real　scenery　dataset.　The　experimental　results　show　that　the　proposed　methods　obviously　outperform　other　state-of-the-art　methods.