Selecting the Optimal Hidden Layer of Extreme Learning Machine Using Multiple Kernel Learning

Abstract

Extreme learning machine (ELM) is emerging as a powerful machine learning method in a variety of application scenarios due to its promising advantages of high accuracy, fast learning speed and easy of implementation. However, how to select the optimal hidden layer of ELM is still an open question in the ELM community. Basically, the number of hidden layer nodes is a sensitive hyperparameter that significantly affects the performance of ELM. To address this challenging problem, we propose to adopt multiple kernel learning (MKL) to design a multi-hidden-layer-kernel ELM (MHLK-ELM). Specifically, we first integrate kernel functions with random feature mapping of ELM to design a hidden-layer-kernel ELM (HLK-ELM), which serves as the base of MHLK-ELM. Then, we utilize the MKL method to propose two versions of MHLK-ELMs, called sparse and non-sparse MHLK-ELMs. Both two types of MHLK-ELMs can effectively find out the optimal linear combination of multiple HLK-ELMs for different classification and regression problems. Experimental results on seven data sets, among which three data sets are relevant to classification and four ones are relevant to regression, demonstrate that the proposed MHLK-ELM achieves superior performance compared with conventional ELM and basic HLK-ELM.