Co-clustering　is　to　group　features　and　samples　simultaneously　and　has　received　increasing　attention　in　data　mining　and　machine　learning,　particularly　in　text　document　categorization　and　gene　expression.　In　this　paper,　two　effective　co-clustering　algorithms　are　proposed　to　exploit　the　joint　advantages　of　local　learning　and　matrix　factorization.　First,　the　co-clustering　problem　is　formulated　as　a　form　of　matrix　tri-factorization　which　embeds　local　structure　learning　and　orthogonality　constraints　for　clustering　indicators.　Using　high-order　matrix　factorization,　an　effective　algorithm　is　proposed　for　co-clustering　problems　and　its　convergence　is　proved.　Second,　symmetric　co-clustering　problems　are　studied,　where　the　sample　affinity　matrix　serves　as　the　input　matrix.　Analogous　high-order　matrix　factorization　is　used　to　develop　an　effective　convergent　algorithm　for　that　problem.　Finally,　the　two　proposed　algorithms　are　validated　in　eight　publicly　available　real-world　datasets　from　machine　learning　repository.　Extensive　experiments　demonstrate　that　the　proposed　algorithms　achieve　competitive　performance　over　existing　state-of-the-art　co-clustering　methods　in　all　tested　datasets.　(C)　2017　Elsevier　B.V.　All　rights　reserved.