The　sheer　size　of　modern　datasets　has　led　to　an　urgent　need　for　summarization　techniques　that　can　identify　representative　elements　of　the　data　set.　Fortunately,　the　vast　majority　of　data　summarization　tasks　satisfy　an　intuitive　diminishing　returns　condition　known　as　submodularity,　which　allows　us　to　find　nearly-optimal　solutions　in　linear　time.　However,　for　many　applications　in　practice,　including　experimental　design　and　sparse　Gaussian　processes,　the　objective　is　in　general　not　submodular.　To　solve　these　optimization　problems,　an　important　research　method　is　to　describe　the　characteristics　of　the　non-submodular　functions.　The　non-submodular　function　is　a　hot　research　topic　in　the　study　of　nonlinear　combinatorial　optimizations.　In　this　paper,　we　combine　and　generalize　the　curvature　and　the　generic　submodularity　ratio　to　design　an　approximation　algorithm　for　two-stage　non-submodular　maximization　under　a　matroid　constraint.　©　2023　Elsevier　B.V.