中文摘要：

针对回归和分类问题,提出一种极限学习机（Extreme Learning Machine,ELM）的快速留一交叉验证算法,并从理论和数值仿真两方面说明其有效性.结果表明,该算法避免了以训练样本数量N次的ELM模型的显式训练,其计算复杂度与N仅呈线性趋势增长,即O（N）.即使在处理大型数据集建模问题时,该算法仍然可以快速地进行ELM模型的选择和评价.通过人工和实际数据集上的仿真实验,验证了该快速留一交叉验证算法的有效性.

英文摘要：

Leave-one-out cross-validation has proved to be near capable of giving the unbiased estimation of the generalization performance of statistical models,and thus can provide a reliable criterion for model selection and comparison.For this reason,the current paper presented a fast leave-one-out cross-validation algorithm in the framework of extreme learning machines（ELMs） with respect to both regression and classification problems,which can avoid training explicitly and just has the complexity of O（N） for a data set with N points.The validity of the algorithm is also strictly proved.The simulations conducted on the artificial and real-world problems show the effectiveness and efficiency of the proposed algorithm.