Deep　neural　mapping　support　vector　machine　(DNMSVM)　has　achieved　good　results　in　numerous　tasks　by　mapping　the　input　from　a　low-dimensional　space　to　a　high-dimensional　space　and　then　using　support　vector　machine　for　classification.　However,　it　did　not　consider　the　connection　of　different　spaces　and　increased　the　model　parameters.　To　improve　the　classification　performance　while　reducing　the　number　of　model　parame-ters,　we　propose　a　deep　Convolutional　Cross-connected　Kernel　Mapping　Support　Vector　Machine　framework　based　on　SelectDropout　(CCKMSVM-SD).　It　consists　of　a　feature　extraction　module　and　a　classification　module.　The　feature　extraction　module　maps　the　data　from　low-dimensional　to　high-dimensional　space　by　fusing　the　representations　of　dif-ferent　dimensional　spaces　through　convolutional　layers　with　cross-connections.　For　some　convolutional　layers,　we　use　the　depthwise　separable　convolution　to　replace　the　original　convolution　to　reduce　the　number　of　parameters.　Besides,　we　use　SelectDropout　to　improve　its　generalization　capability.　The　classification　module　uses　a　soft　margin　support　vector　machine　for　classification.　The　results　on　three　tasks　with　ten　different　datasets　indi-cate　that　CCKMSVM-SD　obtains　higher　classification　accuracy　than　other　models　with　fewer　parameters,　demonstrating　its　effectiveness.(c)　2023　Elsevier　Inc.　All　rights　reserved.