Reduce Training Error of Extreme Learning Machine by Selecting Appropriate Hidden Layer Output Matrix

Extreme learning machine(ELM)is a feedforward neural network with a single layer of hidden nodes,where the weight and the bias connecting input to hidden nodes are randomly assigned.The output weight between hidden nodes and outputs are learned by a linear model.It is interesting to ask whether the training error of ELM is significantly affected by the hidden layer output matrix H,because a positive answer will enable us obtain smaller training error from better H.For single hidden layer feedforward neural network(SLFN)with one input neuron,there is significant difference between the training errors of different Hs.We find there is a reliable strong negative rank correlation between the training errors and some singular values of the Moore-Penrose generalized inverse of H.Based on the rank correlation,a selection algorithm is proposed to choose robust appropriate H to achieve smaller training error among numerous Hs.Extensive experiments are carried out to validate the selection algorithm,including tests on real data set.The results show that it achieves better performance in validity,speed and robustness.