Graph-based　semi-supervised　learning　(SSL)　is　one　of　the　most　popular　topics　in　the　past　decades.　Most　conventional　graph-based　SSL　methods　utilize　two　stage-approach　to　infer　the　class　labels　of　the　unlabeled　data,　i.e.　it　firstly　constructs　a　graph　for　capturing　the　geometry　of　data　manifold　and　then　perform　SSL　for　prediction.　However,　it　suffers　from　three　drawbacks:　(1)　the　graph　construction　and　SSL　stages　are　separate.　They　do　not　share　common　information　to　enhance　the　performance　of　classification;　(2)　the　graph　construction　and　SSL　should　be　scalable.　However,　most　methods　mainly　focus　on　the　improvement　of　classification　accuracy　but　neglect　the　computational　cost;　(3)　the　graph　should　also　be　adaptive　and　robust　to　the　parameters　and　datasets.　However,　this　will　usually　increase　computational　cost　making　the　efficiency　cannot　be　guaranteed　simultaneously.　In　this　paper,　we　aim　to　handle　the　above　issues.　To　achieve　adaptiveness　of　SSL,　we　adopt　a　bilinear　low-rank　model　for　graph　construction,　where　the　coefficient　matrix　of　the　low-rank　model　is　calculated　through　an　adaptive　and　efficient　procedure　the　corresponding　constructed　graph　can　capture　the　global　structure　of　data　manifold.　Meriting　from　such　a　graph,　we　then　propose　a　unified　framework　for　scalable　SSL,　where　we　have　involved　the　graph　construction　and　SSL　into　a　unified　optimization　problem.　As　a　result,　the　discriminative　information　learned　by　SSL　can　be　provided　to　improve　the　discriminative　ability　of　graph　construction,　while　the　updated　graph　can　further　enhance　the　classification　results　of　SSL.　Simulation　indicates　that　the　proposed　method　can　achieve　better　classification　and　clustering　performance　compared　with　other　state-of-the-art　graph-based　SSL　methods.　©　2019,　ICST　Institute　for　Computer　Sciences,　Social　Informatics　and　Telecommunications　Engineering.