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 <tex-math id="M1">{document}HK{document}</tex-math>, and the penalty term is denoted by the norm of the function in <tex-math id="M2">{document}HK{document}</tex-math>. 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 <tex-math id="M3">{document}fV{document}</tex-math> of the generalization error can be approximated by the hypothesis space <tex-math id="M4">{document}HK{document}</tex-math>, 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.