Preliminary study on Wilcoxon-norm-based robust extreme learning machine

The fact that the linear estimators using the rank-based Wilcoxon approach in linear regression problems are usually insensitive to outliers is known in statistics. Outliers are the data points that differ greatly from the pattern set by the bulk of the data. Inspired by this fact, Hsieh et al. introduced the Wilcoxon approach into the area of machine learning. They investigated four new learning machines, such as Wilcoxon neural network (WNN), and developed four gradient descent based backpropagation algorithms to train these learning machines. The performances of these machines are better than ordinary nonrobust neural networks in outliers exist tasks. However, it is hard to balance the learning speed and the stability of these algorithms which is inherently the drawback of gradient descent based algorithms. In this paper, a new algorithm is used to train the output weights of single-layer feedforward neural networks (SLFN) with input weights and biases being randomly chosen. This algorithm is called Wilcoxon-norm based robust extreme learning machine or WRELM for short.