SW-ELM: A summation wavelet extreme learning machine algorithm with a priori parameter initialization

Combining neural networks and wavelet theory as an approximation or prediction models appears to be an effective solution in many applicative areas. However, when building such systems, one has to face parsimony problem, i.e., to look for a compromise between the complexity of the learning phase and accuracy performances. Following that, the aim of this paper is to propose a new structure of connectionist network, the Summation Wavelet Extreme Learning Machine (SW-ELM) that enables good accuracy and generalization performances, while limiting the learning time and reducing the impact of a random initialization procedure. SW-ELM is based on an Extreme Learning Machine (ELM) algorithm for fast batch learning, but with dual activation functions in the hidden layer nodes. This enhances dealing with non-linearity in an efficient manner. The initialization phase of wavelets (of hidden nodes) and neural network parameters (of input-hidden layer) is performed a priori, even before data are presented to the model. The whole proposition is illustrated and discussed by performing tests on three issues related to time-series application: an ``input-output'' approximation problem, a one-step ahead prediction problem, and a multi-steps ahead prediction problem. Performances of SW-ELM are benchmarked with ELM, Levenberg Marquardt algorithm for Single Layer Feed Forward Network (SLFN) and ELMAN network on six industrial datasets. Results show the significance of performances achieved by SW-ELM. (c) 2013 Elsevier B.V. All rights reserved.