Skip to main content

Advertisement

Springer Nature Link
Log in

A new variant of restricted Boltzmann machine with horizontal connections

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Restricted Boltzmann machines (RBMs) are successfully employed to construct deep architectures because their power of expression and the inference is tractable and easy. In this paper, we propose a model named self-connected restricted Boltzmann machine (SCRBM), which adds horizontal connections to the hidden layer to enable direct information transfer between hidden units. We present a simple and effective method based on greedy layer-wise procedure of deep learning algorithms to train the model. Under the algorithm, SCRBM has a three-layer architecture. The first hidden layer extracts features from the data, and the second hidden layer is used to stimulate various interactions between units in the layer. Specifically, to stimulate the lateral inhibition that exists in sensory systems, a log sparse item is introduced to the second hidden layer of SCRBM. Our experiments show that the features learned by our algorithm are more vivid and clean than those learned by basic RBM and SparseRBM. Further experiments show the performance of SCRBM outperforms basic RBM and SparseRBM on several widely used datasets in terms of accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. The search region of \(\alpha _0\), \(\lambda\) and \(\alpha _1\) is \([10^{-4}, 10^{-2}]\), \([10^{-3}, 1]\) and \([10^{-3}, 1]\) respectively.

  2. We choose six \(\lambda\) from \((10^{-3},1)\) using log space and decrease the epochs of pre-training and fine-tune stage to 10 in the experiment.

References

  1. McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133

    Article  MathSciNet  Google Scholar 

  2. Widrow B, Hoff ME (1962) Associative storage and retrieval of digital information in networks of adaptive neurons. In: Biological prototypes and synthetic systems, Springer US, pp 160–160

  3. Ren S, He K, Girshick R, Sun J (2015) Faster r-cnn: towards real-time object detection with region proposal networks. In: Advances in neural information processing systems, pp 91–99

  4. Ciresan DC, Giusti A, Gambardella LM, Schmidhuber J (2013) Mitosis detection in breast cancer histology images with deep neural networks. In: Medical image computing and computer-assisted intervention–MICCAI 2013, Springer, Berlin, pp 411–418

  5. Dahl GE, Yu D, Deng L, Acero A (2012) Context-dependent pre-trained deep neural networks for large-vocabulary speech recognition. IEEE Trans Audio Speech Lang Process 20(1):30–42

    Article  Google Scholar 

  6. Dan CC, Giusti A, Gambardella LM, Schmidhuber J (2012) Deep neural networks segment neuronal membranes in electron microscopy images. Adv Neural Inf Process Syst 25:2852–2860

    Google Scholar 

  7. Hinton GE, Deng L, Yu D, Dahl GE, Mohamed A-R, Jaitly N, Senior A, Vanhoucke V, Nguyen P, Sainath TN (2012) Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups. Sig Process Mag IEEE 29(6):82–97

    Article  Google Scholar 

  8. Von der Malsburg C (1973) Self-organization of orientation sensitive cells in the striate cortex. Biol Cybern 14(2):85–100

    Google Scholar 

  9. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554–2558

    Article  MathSciNet  Google Scholar 

  10. Oyedotun OK, Khashman A (2017) Deep learning in vision-based static hand gesture recognition. Neural Comput Appl 28(12):3941–3951

    Article  Google Scholar 

  11. Zhang H, Cao X, Ho JK, Chow TW (2017) Object-level video advertising: an optimization framework. IEEE Trans Ind Inf 13(2):520–531

    Article  Google Scholar 

  12. Minsky ML, Papert SA (1987) Perceptrons-expanded edition: an introduction to computational geometry. MIT Press, Cambridge

    MATH  Google Scholar 

  13. Bengio Y (2009) Learning deep architectures for AI. Found Trends Mach Learn 2:1–55

    Article  Google Scholar 

  14. Werbos PJ (1982) Applications of advances in nonlinear sensitivity analysis. In: System modeling and optimization. Springer, Berlin, pp 762–770

  15. Werbos PJ. Beyond regression: New tools for prediction and analysis in the behavioral sciences, Ph.d. dissertation Harvard University

  16. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(6088):533–536

    Article  Google Scholar 

  17. Bengio Y, Lamblin P, Popovici D, Larochelle H et al (2007) Greedy layer-wise training of deep networks. Adv Neural Inf Process Syst 19:153

    Google Scholar 

  18. Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural Comput 18(7):1527–1554

    Article  MathSciNet  Google Scholar 

  19. Hartline HK, Wagner HG, Ratliff F (1956) Inhibition in the eye of limulus. J Gen Physiol 39(5):651–673

    Article  Google Scholar 

  20. Lee H, Ekanadham C, Ng AY (2008) Sparse deep belief net model for visual area v2. In: Advances in neural information processing systems, vol 20, pp 873–880

  21. Osindero S, Hinton GE (2008) Modeling image patches with a directed hierarchy of markov random fields. In: Advances in neural information processing systems, pp 1121–1128

  22. Larochelle H, Erhan D, Vincent P (2009) Deep learning using robust interdependent codes. In: AISTATS, pp 312–319

  23. Hinton GE, Sejnowski TJ (1986) Learning and relearning in boltzmann machines. Parallel Distrib Process Explor Microstruct Cognit 1:282–317

    Google Scholar 

  24. Memisevic R, Hinton GE (2010) Learning to represent spatial transformations with factored higher-order boltzmann machines. Neural Comput 22(6):1473–1492

    Article  Google Scholar 

  25. Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural Comput 14(8):1771–1800

    Article  Google Scholar 

  26. Goldstein E (2013) Sensation and perception, Cengage Learning

  27. Welling M, Hinton GE (2002) A new learning algorithm for mean field boltzmann machines. In: International conference on artificial neural networks (ICANN’02), Springer, Berlin, pp 351–357

  28. Ranzato M, Boureau YL, Lecun Y (2007) Sparse feature learning for deep belief networks. Adv Neural Inf Process Syst 20:1185–1192

    Google Scholar 

  29. Ji NN, Zhang JS, Zhang CX, Yin QY (2014) Enhancing performance of restricted boltzmann machines via log-sum regularization. Knowl-Based Syst 63:82–96

    Article  Google Scholar 

  30. Melacci S, Belkin M (2011) Laplacian support vector machines trained in the primal. J Mach Learn Res 12:1149–1184

    MathSciNet  MATH  Google Scholar 

  31. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  32. LeCun Y, Huang FJ, Bottou L (2004) Learning methods for generic object recognition with invariance to pose and lighting. In: IEEE computer society conference on computer vision and pattern recognition (CVPR’04), vol 2, IEEE, pp II–97

  33. Decoste D, Scholkopf B (2002) Training invariant support vector machines. Mach Learn 46(1–3):161–190

    Article  Google Scholar 

  34. Williams CK, Agakov FV. An analysis of contrastive divergence learning in gaussian boltzmann machines. Institute for Adaptive and Neural Computation

  35. Teh YW, Welling M, Osindero S, Hinton GE (2003) Energy-based models for sparse overcomplete representations. J Mach Learn Res 4(12):1235–1260

    MathSciNet  MATH  Google Scholar 

  36. Yuille AL (2005) The convergence of contrastive divergences. In: Advances in neural information processing systems, pp 1593–1600

Download references

Acknowledgements

This work is supported by the National Basic Research Program of China (973 Program, No. 2013CB329404), the National Natural Science Foundation of China (Nos. 61572393, 11501049, 11671317, 11131006) and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Guang Shi & Jiangshe Zhang

  2. School of Science, Chang’an University, Xi’an, 710064, People’s Republic of China

    NanNan Ji

  3. School of Mathematics and Information Science, Chang’an University, Xi’an, 710064, People’s Republic of China

    ChangPeng Wang

Authors
  1. Guang Shi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jiangshe Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. NanNan Ji
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. ChangPeng Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jiangshe Zhang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, G., Zhang, J., Ji, N. et al. A new variant of restricted Boltzmann machine with horizontal connections. Neural Comput & Applic 31, 6521–6533 (2019). https://doi.org/10.1007/s00521-018-3460-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-018-3460-y

Keywords