In　sparse　representation　theory,　how　to　construct　a　dictionary　and　update　dictionary　making　the　dictionary　discriminative　is　still　an　open　problem.　In　order　to　solve　this　problem,　a　dictionary　learning　method　was　presented　based　on　relationship　between　atoms　and　labels　and　a　matrix　was　built　based　on　the　relationship　between　them.　Then　the　matrix　was　updated　with　the　update　of　the　dictionary　atoms.　The　adaptive　relationship　between　atoms　and　labels　of　the　matrix　was　constructed,　improves　the　discriminant　ability　of　dictionary,　the　necessary　guarantee　for　the　classification　was　provided　later.　This　method　not　only　avoided　the　poor　discriminant　ability　of　the　share　dictionary,　but　also　avoided　the　individual　training　dictionary　method　taking　up　lots　of　time　and　memory　faults.　And　making　use　of　l21　norm　constraining　residual　to　remove　noise,　can　not　only　deal　with　sparse　noise,　but　also　the　non-sparse　noise,　which　is　robust　to　the　noise.　The　experiment　results　show　that　the　proposed　method　has　robustness　and　high　recognition　rate　compared　with　other　dictionary　learning　methods.　©　2017,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.