Skip to main content
Log in

Contractive Slab and Spike Convolutional Deep Belief Network

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Convolutional Deep Belief Network (CDBN) is typically classified into deep generative model. Although CDBN has demonstrated the powerful capacity of feature extraction in unsupervised learning, there still remain diverse challenges in the robust and high-quality feature extraction. This paper designs an advanced hierarchical generative model in order to tackle with these troubles. First, we modify conventional Convolutional Restricted Boltzmann Machine (CRBM) through inducing Gaussian hidden units subsequently following point-wise multiplication with the original binary spike hidden units for high-order feature extraction of the local patch. We theoretically derive entire inferences of this novel model. Second, we attempt to learn more robust features by minimizing L2 norm of the jacobian of the extracted features producing from the modified model as novel regularization trick. This can introduce a localized space contraction benefit for robust feature extraction in turn. Finally, this paper construct a novel deep generative model, Contractive Slab and Spike Convolutional Deep Belief Network (CssCDBN), based on the modified CRBM, in order to learn deeper and more abstract features. The performances on diverse visual tasks indicate that CssCDBN is a more powerful model achieving impressive results over many currently excellent models.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Karpathy A, Toderici G, Shetty S, Leung T, Sukthankar R, Fei-Fei L (2014) Large-scale video classification with convolutional neural networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, IEEE, pp 1725–1732. https://doi.org/10.1109/cvpr.2014.223

  2. Lee H, Grosse R, Ranganath R, Ng AY (2011) Unsupervised learning of hierarchical representations with convolutional deep belief networks. Commun ACM 54(10):95–103. https://doi.org/10.1145/2001269.2001295

    Article  Google Scholar 

  3. Masci J, Meier U, Ciresan D, Schmidhuber J (2011) Stacked convolutional auto-encoders for hierarchical feature extraction. Lect Notes Comput Sci 6791:52–59

    Article  Google Scholar 

  4. Krizhevsky A, Sutskever I, Hinton GE (2017) ImageNet classification with deep convolutional neural networks. Commun ACM 60(6):84–90. https://doi.org/10.1145/3065386

    Article  Google Scholar 

  5. Szegedy C, Liu W, Jia YQ, Sermanet P, Reed S, Anguelov D, Erhan D, Vanhoucke V, Rabinovich A (2015) Going deeper with convolutions. In: Proceedings of the IEEE conference on computer vision and pattern recognition, IEEE, pp 1-9

  6. He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, IEEE, pp 770–778

  7. Norouzi M, Ranjbar M, Mori G (2009) Stacks of convolutional restricted boltzmann machines for shift-invariant feature learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, IEEE, pp 2727–2734

  8. Lee H, Largman Y, Pham P, Ng AY (2009) Unsupervised feature learning for audio classification using convolutional deep belief networks. In: Proceedings of the international conference on neural information processing systems, pp 1096–1104

  9. Schmidt EM, Kim YE (2011) Learning Emotion-based acoustic features with deep belief networks. In: 2011 IEEE workshop on applications of signal processing to audio and acoustics (Waspaa), pp 65–68

  10. Liu Y, Zhou SS, Chen QC (2011) Discriminative deep belief networks for visual data classification. Pattern Recogn 44(10–11):2287–2296. https://doi.org/10.1016/j.patcog.2010.12.012

    Article  MATH  Google Scholar 

  11. Bengio Y, Lamblin P, Popovici D, Larochelle H (2006) Greedy layer-wise training of deep networks. In: Proceedings of the international conference on neural information processing systems, pp 153–160

  12. Krizhevsky A (2009) Learning multiple layers of features from tiny images. Science Department, University of Toronto, Tech, pp 1–60. https://doi.org/10.1.1.222.9220

  13. Ranzato M, Krizhevsky A, Hinton GE (2010) Factored 3-way restricted boltzmann machines for modeling natural images. J Mach Learn Res 9:621–628

    Google Scholar 

  14. Swersky K, Ranzato M, Buchman D, Marlin BM, Freitas ND (2011) On autoencoders and score matching for energy based models. In: Proceedings of the international conference on machine learning, pp 1201–1208

  15. Courville A, Bergstra J, Bengio Y (2011) A spike and slab restricted Boltzmann machine. In: Proceedings of the fourteenth international conference on artificial intelligence and statistics, pp 233–241

  16. Bengio Y, Courville A, Bergstra JS (2011) Unsupervised models of images by spike-and-slab RBMs. In: Proceedings of the 28th international conference on machine learning, pp 1145–1152

  17. Rifai S, Vincent P, Muller X, et al (2011) Contractive auto-encoders: explicit invariance during feature extraction. In: Proceedings of the 28th international conference on machine learning, pp 833–840

  18. Lin M, Chen Q, Yan S (2014) Network in network. In: Proceeding of international conference on learning representations

  19. Ranzato MHG (2010) Modeling pixel means and covariances using factorized third-order Boltzmann machines. Proc IEEE Conf Comput Vis Patt Recogn, IEEE 119:2551–2558

    Google Scholar 

  20. Chen D, Lv J, Zhang Y (2017) Graph regularized restricted boltzmann machine. IEEE Trans Neural Netw Learn Syst 99:91–99

    Google Scholar 

  21. Tomczak JM, Gonczarek A (2017) Learning invariant features using subspace restricted Boltzmann machine. Neural Process Lett 45(1):173–182. https://doi.org/10.1007/s11063-016-9519-9

    Article  Google Scholar 

  22. Hu JY, Zhang JS, Ji NN, Zhang CX (2017) A new regularized restricted Boltzmann machine based on class preserving. Knowl-Based Syst 123:1–12. https://doi.org/10.1016/j.knosys.2017.02.012

    Article  Google Scholar 

  23. Vincent P, Larochelle H, Bengio Y, et al (2008) Extracting and composing robust features with denoising autoencoders. In: Proceedings of the 25th international conference on machine learning, pp 1096–1103

  24. Bishop C (1995) Training with noise is equivalent to Tikhonov regularization. Neural Comput 7(1):108–116

    Article  Google Scholar 

  25. Bengio Y, Yao L, Alain G, et al (2013) Generalized denoising auto-encoders as generative models. In: Proceedings of the Advances in neural information processing systems, pp 899–907

  26. Vincent P (2011) A connection between score matching and denoising autoencoders. Neural Comput 23(7):1661–1674

    Article  MathSciNet  MATH  Google Scholar 

  27. Fischer A, Igel C (2012) An Introduction to restricted Boltzmann machines. Iberoamerican congress on pattern recognition. Springer, Berlin, pp 14–36

    Google Scholar 

  28. Zhang N, Ding SF, Zhang J, Xue Y (2018) An overview on restricted Boltzmann machines. Neurocomputing 275:1186–1199. https://doi.org/10.1016/j.neucom.2017.09.065

    Article  Google Scholar 

  29. Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural Comput 14(8):1771–1800. https://doi.org/10.1162/089976602760128018

    Article  MATH  Google Scholar 

  30. Ruder S (2016) An overview of gradient descent optimization algorithms. ArXiv preprint arXiv:1609.04747

  31. Dieleman S (2016) https://github.com/Lasagne/Lasagne. Accessed 10 May 2017

  32. Goodfellow IJ, Warde-Farley D, Lamblin P, et al (2013) Pylearn2: a machine learning research library. ArXiv preprint arXiv:1308.4214

  33. Bergstra J, Breuleux O, Bastien F, et al (2010) Theano: a CPU and GPU math compiler in Python. In: Proceedings of 9th Python in science conference, pp. 1–7

  34. Ba JL, Kingma DP (2015) Adam: a method for stochastic optimization. In: Proceedings of international conference on learning representations, 2015. pp 1–13

  35. Hinton GEOS, Bao K (2005) Learning causally linked Markov random fields. Proc Int Workshop Artif Intell Stat 16:128–135

    Google Scholar 

  36. Osindero S, Welling M, Hinton GE (2006) Topographic product models applied to natural scene statistics. Neural Comput 18(2):381–414. https://doi.org/10.1162/089976606775093936

    Article  MathSciNet  MATH  Google Scholar 

  37. Poultney C, Chopra S, Cun YL (2007) Efficient learning of sparse representations with an energy-based model. In: Proceedings of the advances in neural information processing systems, pp 1137–1144

  38. Ito M, Komatsu H (2004) Representation of angles embedded within contour stimuli in area V2 of macaque monkeys. J Neurosci 24(13):3313–3324. https://doi.org/10.1523/Jneurosci.4364-03.2004

    Article  Google Scholar 

  39. Lee H, Ekandham C, Ng AY (2008) Sparse deep belief net model for visual area V2. In: Proceedings of the advances in neural information processing systems, pp 873–880

  40. Huang KZ, Xu ZL, King I, Lyu MR, Campbell C (2009) Supervised self-taught learning: actively transferring knowledge from unlabeled data. In: IJCNN: 2009 international joint conference on neural networks, vols 1–6, p 481

  41. Wang JJ, Yang JC, Yu K, Lv FJ, Huang T, Gong YH (2010) Locality-constrained linear coding for image classification. In: Proceedings of the IEEE conference on computer vision and pattern recognition, IEEE, pp 3360–3367. https://doi.org/10.1109/cvpr.2010.5540018

  42. Sohn K, Jung DY, Lee H, Hero AO (2011) efficient learning of sparse, distributed, convolutional feature representations for object recognition. In: 2011 IEEE international conference on computer vision (ICCV), pp 2643–2650

  43. Li P, Liu Y, Liu GJ, Guo MZ, Pan ZY (2016) A robust local sparse coding method for image classification with Histogram Intersection Kernel. Neurocomputing 184:36–42. https://doi.org/10.1016/j.neucom.2015.07.136

    Article  Google Scholar 

  44. Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. Science 313(5786):504–507. https://doi.org/10.1126/science.1127647

    Article  MathSciNet  MATH  Google Scholar 

  45. Salakhutdinov R, Hinton G (2012) An efficient learning procedure for deep Boltzmann machines. Neural Comput 24(8):1967–2006. https://doi.org/10.1162/NECO_a_00311

    Article  MathSciNet  MATH  Google Scholar 

  46. Ian Goodfellow DW-F, Mirza Mehdi, Courville Aaron, Bengio Yoshua (2013) Maxout networks. PMLR 28(3):1319–1327

    Google Scholar 

  47. Marijn F Stollenga JM, Gomez F, Schmidhuber J (2014) Deep networks with internal selective attention through feedback connections. In: Advances in neural information processing systems, pp 3545–3553

  48. Lee CY, Xie S, Gallagher P, Zhang Z, Tu Z (2015) Deeply-supervised nets. In: AISTATS, pp 562–570

  49. van der Maaten L, Hinton G (2008) Visualizing data using t-SNE. J Mach Learn Res 9:2579–2605

    MATH  Google Scholar 

  50. Larochelle H, Erhen D, Courville A, et al (2007) An empirical evaluation of deep architectures on problems with many factors of variation. In: Proceedings of the 24th international conference on Machine learning, pp 473–480

  51. Nair V, Hinton G (2009) Implicit mixtures of restricted Boltzmann machines. In: Proceedings of the advances in neural information processing systems, pp 1145–1152

  52. Larochelle H, Bengio Y (2008) Classification using discriminative restricted Boltzmann machines. In: Proceedings of international conference on machine learning, pp 536–543

  53. Kihyuk Sohn GZ, Lee Chansoo, Lee Honglak (2013) Learning and selecting features jointly with point-wise gated Boltzmann machines. Proc Int Conf Mach Learn 28(2):217–225

    Google Scholar 

  54. Li Y, Wang D (2017) Learning robust features with incremental auto-encoders. ArXiv preprint arXiv:1705.09476

  55. Zöhrer M, Pernkopf F (2014) General stochastic networks for classification. In: Proceedings of the advances in neural information processing systems, pp 2015–2023

Download references

Acknowledgements

This work is financially supported by the International S&T Cooperation Program of China (Grant No. 2015DFG12150) named as “Key Technology Elements and Demonstrator for Cloud-Assisted, Wireless Networked Ambulatory Supervision (C-Nurse)” and the National Natural Science Foundation of China (Grant No. 61175126). The authors would like to thank the handing Editor and the anonymous reviewers for their careful reading and helpful remarks, which have contributed in improving the quality of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haibo Wang.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (RAR 42889 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, H., Bi, X. Contractive Slab and Spike Convolutional Deep Belief Network. Neural Process Lett 49, 1697–1722 (2019). https://doi.org/10.1007/s11063-018-9897-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9897-2

Keywords

Navigation