Data　clustering　is　an　important　research　topic　in　data　mining　and　signal　processing　communications.　In　all　the　data　clustering　methods,　the　subspace　spectral　clustering　methods　based　on　self　expression　model,　e.g.,　the　Sparse　Subspace　Clustering　(SSC)　and　the　Low　Rank　Representation　(LRR)　methods,　have　attracted　a　lot　of　attention　and　shown　good　performance.　The　key　step　of　SSC　and　LRR　is　to　construct　a　proper　affinity　or　similarity　matrix　of　data　for　spectral　clustering.　Recently,　Laplacian　graph　constraint　was　introduced　into　the　basic　SSC　and　LRR　and　obtained　considerable　improvement.　However,　the　current　graph　construction　methods　do　not　well　exploit　and　reveal　the　non-linear　properties　of　the　clustering　data,　which　is　common　for　high　dimensional　data.　In　this　paper,　we　introduce　the　classic　manifold　learning　method,　the　Local　Linear　Embedding　(LLE),　to　learn　the　non-linear　structure　underlying　the　data　and　use　the　learned　local　geometry　of　manifold　as　a　regularization　for　SSC　and　LRR,　which　results　the　proposed　LLE-SSC　and　LLE-LRR　clustering　methods.　Additionally,　to　solve　the　complex　optimization　problem　involved　in　the　proposed　models,　an　efficient　algorithm　is　also　proposed.　We　test　the　proposed　data　clustering　methods　on　several　types　of　public　databases.　The　experimental　results　show　that　our　methods　outperform　typical　subspace　clustering　methods　with　Laplacian　graph　constraint.