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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 267478, 12 pages
Research Article

Topologically Ordered Feature Extraction Based on Sparse Group Restricted Boltzmann Machines

1School of Computer Science and Technology, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
2State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
3Engineering Research Center for Spatio-Temporal Data Smart Acquisition and Application, Ministry of Education of China, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
4Institute of Information Technology, Luoyang Normal University, 71 Luolong Road, Luoyang 471022, China

Received 20 March 2015; Revised 28 July 2015; Accepted 9 September 2015

Academic Editor: Panos Liatsis

Copyright © 2015 Zhong Chen 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.


How to extract topologically ordered features efficiently from high-dimensional data is an important problem of unsupervised feature learning domains for deep learning. To address this problem, we propose a new type of regularization for Restricted Boltzmann Machines (RBMs). Adding two extra terms in the log-likelihood function to penalize the group weights and topologically ordered factors, this type of regularization extracts topologically ordered features based on sparse group Restricted Boltzmann Machines (SGRBMs). Therefore, it encourages an RBM to learn a much smoother probability distribution because its formulations turn out to be a combination of the group weight-decay and topologically ordered factor regularizations. We apply this proposed regularization scheme to image datasets of natural images and Flying Apsara images in the Dunhuang Grotto Murals at four different historical periods. The experimental results demonstrate that the combination of these two extra terms in the log-likelihood function helps to extract more discriminative features with much sparser and more aggregative hidden activation probabilities.