Constructing　tensor　with　low-rank　prior　is　the　crucial　issue　of　tensor　based　multi-view　subspace　clustering　methods,　but　there　are　still　some　shortcomings.　First,　they　cannot　adaptively　allocate　the　contribution　of　different　views,　resulting　in　the　learned　tensor　being　suboptimal.　Second,　they　pursue　low-rank　tensor　for　different　data　through　Discrete　Fourier　Transform　based　tensor　nuclear　norm,　which　lacks　generality.　To　overcome　these　problems,　we　propose　an　invertible　linear　transforms　based　adaptive　multi-view　subspace　clustering　method,　named　ILTMSC.　Firstly,　we　mine　the　potential　low-order　representation　of　each　view　through　self-representation　subspace　learning.　Then,　we　capture　high-order　representation　by　integrating　low-order　representations　with　adaptive　weights　into　a　tensor　and　then　rotated.　This　strategy　can　integrate　tensor　adaptively　and　handle　the　noise　effectively.　Finally,　we　approximate　the　low-rank　tensor　with　a　recently　proposed　invertible　linear　transforms　based　tensor　nuclear　norm.　Such　a　new　tensor　nuclear　norm　makes　our　model　more　general　because　it　can　use　different　invertible　linear　transforms　for　different　tensor　data.　Moreover,　an　adaptive　weighted　tensor　singular　value　thresholding　operator　is　proposed　for　capturing　the　new　tensor　nuclear　norm.　Our　model　could　be　solved　by　convex　optimization　efficiently.　Extensive　experiments　on　multi-view　datasets　validate　the　effectiveness　and　robustness　of　our　method.　©　2023　Elsevier　B.V.