Incremental extreme learning machine with fully complex hidden nodes

Huang et al. [Universal approximation using incremental constructive feedforward networks with random hidden nodes, IEEE Trans. Neural Networks 17(4) (2006) 879–892] has recently proposed an incremental extreme learning machine (I-ELM), which randomly adds hidden nodes incrementally and analytically determines the output weights. Although hidden nodes are generated randomly, the network constructed by I-ELM remains as a universal approximator. This paper extends I-ELM from the real domain to the complex domain. We show that, as long as the hidden layer activation function is complex continuous discriminatory or complex bounded nonlinear piecewise continuous, I-ELM can still approximate any target functions in the complex domain. The universal capability of the I-ELM in the complex domain is further verified by two function approximations and one channel equalization problems.