Universal Approximation and QoS Violation Application of Extreme Learning Machine

Neural networks have been successfully applied to many applications due to their approximation capability. However, complicated network structures and algorithms will lead to computational and time-consuming burdens. In order to satisfy demanding real-time requirements, many fast learning algorithms were explored in the past. Recently, a fast algorithm, Extreme Learning Machine (ELM) (Huang et al. 70:489–501, 2006) was proposed. Unlike conventional algorithms whose neurons need to be tuned, the input-to-hidden neurons of ELM are randomly generated. Though a large number of experimental results have shown that input-to-hidden neurons need not be tuned, there lacks a rigorous proof whether ELM possesses the universal approximation capability. In this paper, based on the universal approximation property of an orthonormal method, we firstly illustrate the equivalent relationship between ELM and the orthonormal method, and further prove that neural networks with ELM are also universal approximations. We also successfully apply ELM to the identification of QoS violation in the multimedia transmission.