Multi-view　subspace　approaches　have　been　extensively　studied　for　their　ability　to　project　data　onto　a　low-dimensional　space,　which　is　in　favour　of　the　clustering　task.　However,　most　existing　models　mainly　concentrate　on　reconstructing　data　from　the　sample　space,　neglecting　crucial　information　from　the　feature　space,　and　failing　to　learn　an　optimal　representation.　For　addressing　this　issue,　we　present　a　new　joint　framework,　dubbed　low-rank　tensor　learning　with　projection　distance　metric.　This　model　recovers　the　original　data　by　learning　two　low-rank　factors,　which　thoroughly　exploits　the　essential　data　information.　Specifically,　a　low-rank　constraint　is　introduced　on　a　tensor　that　integrates　subspace　representations　of　all　view　data,　enabling　it　to　capture　high-order　relationships　among　views　while　recovering　data　from　the　sample　space.　Meanwhile,　a　low-rank　projection　matrix　calculated　by　decomposing　the　original　features　is　utilized　to　enhance　data　structures　via　exploring　relationships　among　feature　dimensions.　Additionally,　a　distance　metric　learned　by　the　projection　matrix　is　introduced　to　leverage　the　local　structure　embedded　in　samples,　thereby　encouraging　the　learned　representation　to　be　more　discriminative.　Extensive　experimental　results　on　six　datasets　indicate　the　superiority　of　the　proposed　model.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.