Abstract: An extrme learning machine(ELM) algorithm based on wavelet transform was designed for a class of indentification and regression problem with inhomogeneity in a space. From the standpoint of multiresolution analysis,a set of compactly supported orthogonal wavelets was constructed as the hidden layer activation function,and the output layer weight of the network was trained by an error minimized extreme learning machine. This method avoided retraining the output layer parameter as adding a subnetwork with higher resolution. The wavelet ELM was then extended into a two-dimensional space using the tensor product of a scaling function. To hurdle high-dimensionality issues,ridgelet transform based on ELM was obtained,whose scaling,direction,and position parameters were determined by optimization methods. Simulation results on functions with singularity confirm that the wavelet ELM can approch the target better. When being tested on some real benchmark problems,the ridgelet ELM demonstrates better training and testing accuracy on most cases.