A smooth hidden space support vector machine

Applying the smoothing techniques to the support vector machine in the hidden space, a smooth hidden space support vector machine (SHSSVM) is presented with some distinct mathematical features, such as the strong convexity and infinite differentiability. Beyond that, SHSSVM broadens the area of admissible kernel functions, where any real-valued symmetry function can be used as the hidden function, including the Mercer kernels and their combinations. Firstly, the input data are transformed to the hidden space by a hidden function. Secondly, the smoothing technique is utilized to derive the unconstrained smooth model. Finally, the Newton algorithm is introduced to figure out the optimal solution. The numerical experiments on benchmark data demonstrate that SHSSVM has much higher training accuracies than HSSVM and SSVM, but with much lower training time.