a b s t r a c t: 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 highdimensional 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 parameters, 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 different 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 indicate that CCKMSVM-SD obtains higher classification accuracy than other models with fewer parameters, demonstrating its effectiveness.