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Mathematical Problems in Engineering
Volume 2014, Article ID 395686, 12 pages
Research Article

RMSE-ELM: Recursive Model Based Selective Ensemble of Extreme Learning Machines for Robustness Improvement

1School of Information and Engineering, Ocean University of China, Shandong, Qingdao 266000, China
2School of Mechanical and Electrical Engineering, China Jiliang University, Zhejiang, Hangzhou 310018, China
3Department of Mechanical and Industrial Engineering and the Iowa Informatics Initiative, The University of Iowa, Iowa City, IA 52242-1527, USA
4Arcada University of Applied Sciences, 00550 Helsinki, Finland

Received 7 August 2014; Revised 14 September 2014; Accepted 22 September 2014; Published 9 October 2014

Academic Editor: Tao Chen

Copyright © 2014 Bo Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For blended data, the robustness of extreme learning machine (ELM) is so weak because the coefficients (weights and biases) of hidden nodes are set randomly and the noisy data exert a negative effect. To solve this problem, a new framework called “RMSE-ELM” is proposed in this paper. It is a two-layer recursive model. In the first layer, the framework trains lots of ELMs in different ensemble groups concurrently and then employs selective ensemble approach to pick out an optimal set of ELMs in each group, which can be merged into a large group of ELMs called candidate pool. In the second layer, selective ensemble approach is recursively used on candidate pool to acquire the final ensemble. In the experiments, we apply UCI blended datasets to confirm the robustness of our new approach in two key aspects (mean square error and standard deviation). The space complexity of our method is increased to some degree, but the result has shown that RMSE-ELM significantly improves robustness with a rapid learning speed compared to representative methods (ELM, OP-ELM, GASEN-ELM, GASEN-BP, and E-GASEN). It becomes a potential framework to solve robustness issue of ELM for high-dimensional blended data in the future.