Error analysis of classification learning algorithms based on LUMs loss

In this paper, we study the learning performance of regularized large-margin unified machines (LUMs) for classification problem. The hypothesis space is taken to be a reproducing kernel Hilbert space \begin{document}$ {\mathcal H}_K $\end{document}, and the penalty term is denoted by the norm of the function in \begin{document}$ {\mathcal H}_K $\end{document}. Since the LUM loss functions are differentiable and convex, so the data piling phenomena can be avoided when dealing with the high-dimension low-sample size data. The error analysis of this classification learning machine mainly lies upon the comparison theorem [3] which ensures that the excess classification error can be bounded by the excess generalization error. Under a mild source condition which shows that the minimizer \begin{document}$ f_V $\end{document} of the generalization error can be approximated by the hypothesis space \begin{document}$ {\mathcal H}_K $\end{document}, and by a leave one out variant technique proposed in [13], satisfying error bound and learning rate about the mean of excess classification error are deduced.