ELM in nonstationary environment: Extreme Learning Machine and its variants for Time-Varying Neural Networks case study

System identification in nonstationary environment represents a challenging problem and an advaned neural architecture namely Time-Varying Neural Net- works (TV-NN) has shown remarkable identification properties in nonlinear and nonstationary conditions. Time-varying weights, each being a linear com- bination of a certain set of basis functions, are used in such kind of networks instead of stable ones, which inevitalbly increases the number of free parame- ters. Therefore, an Extreme Learning Machine (ELM) approach is developed to accelerate the training procedure for TV-NN. What is more, in order to ob- tain a more compact structure, or determine several important parameters, or update the network more efficiently in online case, several variants of ELM-TV are proposed and discussed in the book. Related computer simulations have been carried out and show the effectiveness of the algorithms.