Kernel support matrix machines with ramp loss

To overcome the shortcomings of classical support vector machines in classifying matrix-type data and outliers, we aim at studying kernel support matrix machines with ramp loss. For this purpose, a class of proximal stationary points is introduced. First, the relationship between the proximal stationary point, the Karush-Kuhn-Tucker point, and the locally optimal solution to the proposed model is built. Second, to solve the kernel support matrix machines with ramp loss, an alternating direction method of multipliers algorithm is developed. Any limit point of the sequence generated by this algorithm is shown to be a proximal stationary point. Finally, through extensive numerical simulations, we showcase the superiority of the proposed model with convolutional neural tangent kernels over existing state-of-the-art methods for matrix input data. © 2025 World Scientific Publishing Company.