An analysis of ELM approximate error based on random weight matrix

It is experimentally observed that the approximate errors of extreme learning machine (ELM) are dependent on the uniformity of training samples after the network architecture is fixed, and the uniformity, which is usually measured by the variance of distances among samples, varies with the linear transformation induced by the random weight matrix. By analyzing the dimension increase process in ELM, this paper gives an approximate relation between the uniformities before and after the linear transformation. Furthermore, by restricting ELM with a two-dimensional space, it gives an upper bound of ELM approximate error which is dependent on the distributive uniformity of training samples. The analytic results provide some useful guidelines to make clear the impact of random weights on ELM approximate ability and improve ELM prediction accuracy.