Robust Fisher-regularized extreme learning machine with asymmetric Welsch-induced loss function for classification

In general, it is a worth challenging problem to build a robust classifier for data sets with noises or outliers. Establishing a robust classifier is a more difficult problem for datasets with asymmetric noise distribution. The Fisher-regularized extreme learning machine (Fisher-ELM) considers the statistical knowledge of the data, however, it ignores the impact of noises or outliers. In this paper, to reduce the negative influence of noises or outliers, we first put forward a novel asymmetric Welsch loss function named AW-loss based on asymmetric L 2 -loss function and Welsch loss function. Based on the AW-loss function, we then present a new robust Fisher-ELM called AWFisher-ELM. The proposed AWFisher-ELM not only takes into account the statistical information of the data, but also considers the impact of asymmetric distribution noises. We utilize concave-convex procedure (CCCP) and dual method to solve the non-convexity of the proposed AWFisher-ELM. Simultaneously, an algorithm for AWFisher-ELM is given and a theorem about the convergence of the algorithm is proved. To validate the effectiveness of our algorithm, we compare our AWFisher-ELM with the other state-of-the-art methods on artificial data sets, UCI data sets, NDC large data sets and image data sets by setting different ratios of noises. The experimental results are as follows, the accuracy of AWFisher-ELM is the highest in the artificial data sets, reaching 98.9%. For the large-scale NDC data sets and the image data sets, the accuracy of AWFisher-ELM is also the highest. For the ten UCI data sets, the accuracy and F 1 value of AWFisher-ELM are the highest in most data sets expect for Diabetes. In terms of training time, our AWFisher-ELM has almost the same training time with RHELM and CHELM, but it takes longer time than OPT-ELM, WCS-SVM, Fisher-SVM, Pinball-FisherSVM, and Fisher-ELM. This is because AWFisher-ELM, RHELM, and CHELM need to solve a convex quadratic subprogramming problem in each iteration. In conclusion, our method exhibits excellent generalization performance expect for the longer training time.