Extreme Learning Machines [1]–[4] (ELM) as important emergent machine learning techniques, are proposed for both ‘‘generalized’’ Single-Layer Feed-forward Networks (SLFNs) [1], [3], [5]–[7] and multi layered feedforward networks [6]. Unlike traditional learning theories and learning algorithms, ELM theories show that hidden neurons need not be tuned in learning and their parameters can be independent of the training data, but nevertheless ELMs have universal approximation and clas- sification properties [5]–[7]. In most cases, the ELM hidden neurons can be randomly generated, which means that all the parameters of the hidden neurons (e.g., the input weights and biases of additive neurons, the centres and the impact factors of RBF nodes, frequencies and the shift of Fourier series, etc) can be randomly generated and therefore also independent of the training data. Some related efforts had been attempted before [8]–[10] with parts of SLFN generated randomly or taken from a subset of data samples [11], however, they either lack proof of the universal approximation capability for fully randomized hidden neurons, or can be considered as specific cases of ELM [12].
ELM, consisting of a wide type of feed forward neural networks, is the first method [6], [7], which can univer- sally approximate any continuous function with almost any nonlinear and piecewise continuous hidden neurons.