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Mathematical Problems in Engineering
Volume 2016, Article ID 1649486, 17 pages
Research Article

Deep Network Based on Stacked Orthogonal Convex Incremental ELM Autoencoders

College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

Received 1 March 2016; Revised 7 May 2016; Accepted 31 May 2016

Academic Editor: Lotfi Senhadji

Copyright © 2016 Chao Wang 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.


Extreme learning machine (ELM) as an emerging technology has recently attracted many researchers’ interest due to its fast learning speed and state-of-the-art generalization ability in the implementation. Meanwhile, the incremental extreme learning machine (I-ELM) based on incremental learning algorithm was proposed which outperforms many popular learning algorithms. However, the incremental algorithms with ELM do not recalculate the output weights of all the existing nodes when a new node is added and cannot obtain the least-squares solution of output weight vectors. In this paper, we propose orthogonal convex incremental learning machine (OCI-ELM) with Gram-Schmidt orthogonalization method and Barron’s convex optimization learning method to solve the nonconvex optimization problem and least-squares solution problem, and then we give the rigorous proofs in theory. Moreover, in this paper, we propose a deep architecture based on stacked OCI-ELM autoencoders according to stacked generalization philosophy for solving large and complex data problems. The experimental results verified with both UCI datasets and large datasets demonstrate that the deep network based on stacked OCI-ELM autoencoders (DOC-IELM-AEs) outperforms the other methods mentioned in the paper with better performance on regression and classification problems.