In　this　paper,　we　propose　semi-supervised　kernel　matrix　learning　(SS-KML)　using　adaptive　constraint　based　seed　propagation　(ACSP).　Conventional　SS-KML　methods　such　as　pairwise　constraint　propagation　(PCP)　and　kernel　propagation　(KP)　have　achieved　outstanding　performance　in　data　classification.　However,　they　are　likely　to　distort　the　global　data　structure　because　of　using　hard　constraints　in　their　semi-definite　problems　(SDPs)　for　constraint　propagation.　Moreover,　given　a　large　number　of　pairwise　constraints　and　a　large　amount　of　samples,　they　tend　to　be　incredibly　complex,　thus　being　hard　to　be　applied　to　real　life　complex　problems　such　as　internet-scale　image　categorization.　To　address　this　problem,　we　utilize　adaptive　constraints　to　effectively　maintain　the　inherent　coherence　of　samples　and　successfully　propagate　constraint　information　into　all　samples.　Moreover,　we　adopt　seed　propagation　to　remarkably　reduce　the　computational　complexity　of　SS-KML.　Experimental　results　demonstrate　that　ACSP　achieves　a　significant　improvement　in　performance　over　PCP　and　KP　in　terms　of　both　effectiveness　and　efficiency.　(c)　2020　Published　by　Elsevier　Ltd.