The　choice　of　kernel　has　an　important　effect　on　the　performance　of　a　support　vector　machine　(SVM).　The　effect　could　be　reduced　by　NEUROSVM,　an　architecture　using　multilayer　perceptron　for　feature　extraction　and　SVM　for　classification.　In　binary　classification,　a　general　linear　kernel　NEUROSVM　can　be　theoretically　simplified　as　an　input　layer,　many　hidden　layers,　and　an　SVM　output　layer.　As　a　feature　extractor,　the　sub-network　composed　of　the　input　and　hidden　layers　is　first　trained　together　with　a　virtual　ordinary　output　layer　by　backpropagation,　then　with　the　output　of　its　last　hidden　layer　taken　as　input　of　the　SVM　classifier　for　further　training　separately.　By　taking　the　sub-network　as　a　kernel　mapping　from　the　original　input　space　into　a　feature　space,　we　present　a　novel　model,　called　deep　neural　mapping　support　vector　machine　(DNMSVM),　from　the　viewpoint　of　deep　learning.　This　model　is　also　a　new　and　general　kernel　learning　method,　where　the　kernel　mapping　is　indeed　an　explicit　function　expressed　as　a　sub-network,　different　from　an　implicit　function　induced　by　a　kernel　function　traditionally.　Moreover,　we　exploit　a　two-stage　procedure　of　contrastive　divergence　learning　and　gradient　descent　for　DNMSVM　to　jointly　training　an　adaptive　kernel　mapping　instead　of　a　kernel　function,　without　requirement　of　kernel　tricks.　As　a　whole　of　the　sub-network　and　the　SVM　classifier,　the　joint　training　of　DNMSVM　is　done　by　using　gradient　descent　to　optimize　the　objective　function　with　the　sub-network　layer-wise　pre-trained　via　contrastive　divergence　learning　of　restricted　Boltzmann　machines.　Compared　to　the　separate　training　of　NEUROSVM,　the　joint　training　is　a　new　algorithm　for　DNMSVM　to　have　advantages　over　NEUROSVM.　Experimental　results　show　that　DNMSVM　can　outperform　NEUROSVM　and　RBFSVM　(i.e.,　SVM　with　the　kernel　of　radial　basis　function),　demonstrating　its　effectiveness.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.