Existing　subspace　clustering　methods　usually　rest　on　a　global　linear　data　set,　which　expresses　each　data　point　as　a　linear　combination　of　all　other　data　points,　and　thus　common　methods　are　not　well　suited　for　the　nonlinear　data.　To　overcome　this　limitation,　the　local　sparse　subspace　clustering　and　local　least　squares　regression　subspace　clustering　are　proposed.　The　idea　of　the　two　new　methods　comes　from　manifold　learning　which　expresses　each　data　point　as　a　linear　combination　of　its　k　nearest　neighbors,　and　is　combined　with　sparse　subspace　clustering　and　least　squares　subspace　clustering　respectively.　Experimental　results　show　that　our　method　is　effective　on　two-moon　synthetic　data,　six　image　data　sets　and　four　gene　expression　data　sets.　Copyright　©　2016　Acta　Automatica　Sinica.　All　rights　reserved.