UCI dataset.

ELM (Extreme learning machine) has drawn great attention due its high training speed and outstanding generalization performance. To solve the problem that the long training time of kernel ELM auto-encoder and the difficult setting of the weight of kernel function in the existing multi-kernel models, a multi-kernel cost-sensitive ELM method based on expectation kernel auto-encoder is proposed. Firstly, from the view of similarity, the reduced kernel auto-encoder is defined by randomly selecting the reference points from the input data; then, the reduced expectation kernel auto-encoder is designed according to the expectation kernel ELM, and the combination of random mapping and similarity mapping is realized. On this basis, two multi-kernel ELM models are designed, and the output of the classifier is converted into posterior probability. Finally, the cost-sensitive decision is realized based on the minimum risk criterion. The experimental results on the public and realistic datasets verify the effectiveness of the method.

极限学习机（Extreme learning machine，ELM）凭借其极快的训练速度与优异的泛化性能受到广泛关注。针对现有多核模型（multi-kernel models）中核极限学习机自编码器（kernel ELM auto-encoder）训练耗时过长、核函数权重难以设置的问题，本文提出一种基于期望核自编码器（expectation kernel auto-encoder）的代价敏感多核极限学习机方法。首先，从相似度视角出发，通过从输入数据中随机选取参考点定义约简核自编码器（reduced kernel auto-encoder）；随后基于期望核极限学习机（expectation kernel ELM）设计约简期望核自编码器（reduced expectation kernel auto-encoder），实现随机映射与相似度映射的结合。在此基础上构建两款多核极限学习机模型（multi-kernel ELM models），并将分类器的输出转换为后验概率（posterior probability）。最终基于最小风险准则（minimum risk criterion）实现代价敏感决策（cost-sensitive decision）。在公开真实数据集上开展的实验结果验证了所提方法的有效性。