This　article　proposes　a　novel　low-rank　matrix　factorization　model　for　semisupervised　image　clustering.　In　order　to　alleviate　the　negative　effect　of　outliers,　the　maximum　correntropy　criterion　(MCC)　is　incorporated　as　a　metric　to　build　the　model.　To　utilize　the　label　information　to　improve　the　clustering　results,　a　constraint　graph　learning　framework　is　proposed　to　adaptively　learn　the　local　structure　of　the　data　by　considering　the　label　information.　Furthermore,　an　iterative　algorithm　based　on　Fenchel　conjugate　(FC)　and　block　coordinate　update　(BCU)　is　proposed　to　solve　the　model.　The　convergence　properties　of　the　proposed　algorithm　are　analyzed,　which　shows　that　the　algorithm　exhibits　both　objective　sequential　convergence　and　iterate　sequential　convergence.　Experiments　are　conducted　on　six　real-world　image　datasets,　and　the　proposed　algorithm　is　compared　with　eight　state-of-the-art　methods.　The　results　show　that　the　proposed　method　can　achieve　better　performance　in　most　situations　in　terms　of　clustering　accuracy　and　mutual　information.