Skip to main content

Convolutional Neural Networks

Abstract

Convolutional neural networks are designed to work with grid-structured inputs, which have strong spatial dependencies in local regions of the grid. The most obvious example of grid-structured data is a 2-dimensional image. This type of data also exhibits spatial dependencies, because adjacent spatial locations in an image often have similar color values of the individual pixels. An additional dimension captures the different colors, which creates a 3-dimensional input volume. Therefore, the features in a convolutional neural network have dependencies among one another based on spatial distances.

Keywords

  • Convolution Neural Network
  • AlexNet
  • Convolutional Autoencoder
  • Footprint Parameters
  • Skip Connections

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-94463-0_8
  • Chapter length: 57 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-94463-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)
Hardcover Book
USD   69.99
Price excludes VAT (USA)
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 8.19
Figure 8.20

Notes

  1. 1.

    Here, it is assumed that (L qF q) is exactly divisible by S q in order to obtain a clean fit of the convolution filter with the original image. Otherwise, some ad hoc modifications are needed to handle edge effects. In general, this is not a desirable solution.

  2. 2.

    In recent years, subsampling also refers to other operations that reduce the spatial footprint. Therefore, there is some difference between the classical usage of this term and modern usage.

  3. 3.

    The top-5 error rate makes more sense in image data where a single image might contain objects of multiple classes. Throughout this chapter, we use the term “error rate” to refer to the top-5 error rate.

  4. 4.

    http://www.clarifai.com

  5. 5.

    Personal communication from Matthew Zeiler.

  6. 6.

    The original architecture also contained auxiliary classifiers, which have been ignored in recent years.

  7. 7.

    Typically, a 3 × 3 filter is used at a stride/padding of 1. This trend started with the principles in VGG, and was adopted by ResNet.

  8. 8.

    Under normal circumstances, one only backpropagates to hidden layers as an intermediate step to compute gradients with respect to incoming weights in that hidden layer. Therefore, backpropagation to input layer is never really needed in traditional training. However, backpropagation to the input layer is identical to that with respect to the hidden layers.

  9. 9.

    Example available at http://deeplearning.net/software/theano/tutorial/conv_arithmetic.html.

Bibliography

  1. A. Babenko, A. Slesarev, A. Chigorin, and V. Lempitsky. Neural codes for image retrieval. arXiv:1404.1777, 2014.https://arxiv.org/abs/1404.1777

  2. M. Baccouche, F. Mamalet, C. Wolf, C. Garcia, and A. Baskurt. Sequential deep learning for human action recognition. International Workshop on Human Behavior Understanding, pp. 29–39, 2011.

    Google Scholar 

  3. N. Ballas, L. Yao, C. Pal, and A. Courville. Delving deeper into convolutional networks for learning video representations. arXiv:1511.06432, 2015.https://arxiv.org/abs/1511.06432

  4. T. Brox and J. Malik. Large displacement optical flow: descriptor matching in variational motion estimation. IEEE TPAMI, 33(3), pp. 500–513, 2011.

    CrossRef  Google Scholar 

  5. A. Coates and A. Ng. Learning feature representations with k-means. Neural networks: Tricks of the Trade, Springer, pp. 561–580, 2012.

    Google Scholar 

  6. R. Collobert, J. Weston, L. Bottou, M. Karlen, K. Kavukcuoglu, and P. Kuksa. Natural language processing (almost) from scratch. Journal of Machine Learning Research, 12, pp. 2493–2537, 2011.

    MATH  Google Scholar 

  7. R. Collobert and J. Weston. A unified architecture for natural language processing: Deep neural networks with multitask learning. ICML Conference, pp. 160–167, 2008.

    Google Scholar 

  8. D. Cox and N. Pinto. Beyond simple features: A large-scale feature search approach to unconstrained face recognition. IEEE International Conference on Automatic Face and Gesture Recognition and Workshops, pp. 8–15, 2011.

    Google Scholar 

  9. N. Dalal and B. Triggs. Histograms of oriented gradients for human detection. Computer Vision and Pattern Recognition, pp. 886–893, 2005.

    Google Scholar 

  10. M. Defferrard, X. Bresson, and P. Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. NIPS Conference, pp. 3844–3852, 2016.

    Google Scholar 

  11. J. Donahue, L. Anne Hendricks, S. Guadarrama, M. Rohrbach, S. Venugopalan, K. Saenko, and T. Darrell. Long-term recurrent convolutional networks for visual recognition and description. IEEE conference on computer vision and pattern recognition, pp. 2625–2634, 2015.

    Google Scholar 

  12. C. Dos Santos and M. Gatti. Deep Convolutional Neural Networks for Sentiment Analysis of Short Texts. COLING, pp. 69–78, 2014.

    Google Scholar 

  13. A. Dosovitskiy and T. Brox. Inverting visual representations with convolutional networks. CVPR Conference, pp. 4829–4837, 2016.

    Google Scholar 

  14. V. Dumoulin and F. Visin. A guide to convolution arithmetic for deep learning. arXiv:1603.07285, 2016.https://arxiv.org/abs/1603.07285

  15. P. Felzenszwalb, R. Girshick, D. McAllester, and D. Ramanan. Object detection with discriminatively trained part-based models. IEEE TPAMI, 32(9), pp. 1627–1645, 2010.

    CrossRef  Google Scholar 

  16. K. Fukushima. Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biological Cybernetics, 36(4), pp. 193–202, 1980.

    CrossRef  Google Scholar 

  17. H. Gao, H. Yuan, Z. Wang, and S. Ji. Pixel Deconvolutional Networks. arXiv:1705.06820, 2017.https://arxiv.org/abs/1705.06820

  18. L. Gatys, A. S. Ecker, and M. Bethge. Texture synthesis using convolutional neural networks. NIPS Conference, pp. 262–270, 2015.

    Google Scholar 

  19. L. Gatys, A. Ecker, and M. Bethge. Image style transfer using convolutional neural networks. IEEE Conference on Computer Vision and Pattern Recognition, pp. 2414–2423, 2015.

    Google Scholar 

  20. K. Greff, R. K. Srivastava, and J. Schmidhuber. Highway and residual networks learn unrolled iterative estimation. arXiv:1612.07771, 2016.https://arxiv.org/abs/1612.07771

  21. R. Girshick, F. Iandola, T. Darrell, and J. Malik. Deformable part models are convolutional neural networks. IEEE Conference on Computer Vision and Pattern Recognition, pp. 437–446, 2015.

    Google Scholar 

  22. B. Hariharan, P. Arbelaez, R. Girshick, and J. Malik. Simultaneous detection and segmentation. arXiv:1407.1808, 2014.https://arxiv.org/abs/1407.1808

  23. D. Hassabis, D. Kumaran, C. Summerfield, and M. Botvinick. Neuroscience-inspired artificial intelligence. Neuron, 95(2), pp. 245–258, 2017.

    CrossRef  Google Scholar 

  24. M. Havaei et al. Brain tumor segmentation with deep neural networks. Medical Image Analysis, 35, pp. 18–31, 2017.

    CrossRef  Google Scholar 

  25. K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778, 2016.

    Google Scholar 

  26. K. He, X. Zhang, S. Ren, and J. Sun. Identity mappings in deep residual networks. European Conference on Computer Vision, pp. 630–645, 2016.

    Google Scholar 

  27. M. Henaff, J. Bruna, and Y. LeCun. Deep convolutional networks on graph-structured data. arXiv:1506.05163, 2015.https://arxiv.org/abs/1506.05163

  28. G. Huang, Y. Sun, Z. Liu, D. Sedra, and K. Weinberger. Deep networks with stochastic depth. European Conference on Computer Vision, pp. 646–661, 2016.

    Google Scholar 

  29. G. Huang, Z. Liu, K. Weinberger, and L. van der Maaten. Densely connected convolutional networks. arXiv:1608.06993, 2016.https://arxiv.org/abs/1608.06993

  30. D. Hubel and T. Wiesel. Receptive fields of single neurones in the cat’s striate cortex. The Journal of Physiology, 124(3), pp. 574–591, 1959.

    CrossRef  Google Scholar 

  31. K. Jarrett, K. Kavukcuoglu, M. Ranzato, and Y. LeCun. What is the best multi-stage architecture for object recognition? International Conference on Computer Vision (ICCV), 2009.

    Google Scholar 

  32. S. Ji, W. Xu, M. Yang, and K. Yu. 3D convolutional neural networks for human action recognition. IEEE TPAMI, 35(1), pp. 221–231, 2013.

    CrossRef  Google Scholar 

  33. Y. Jia et al. Caffe: Convolutional architecture for fast feature embedding. ACM International Conference on Multimedia, 2014.

    Google Scholar 

  34. J. Johnson, A. Karpathy, and L. Fei-Fei. Densecap: Fully convolutional localization networks for dense captioning. IEEE Conference on Computer Vision and Pattern Recognition, pp. 4565–4574, 2015.

    Google Scholar 

  35. J. Johnson, A. Alahi, and L. Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. European Conference on Computer Vision, pp. 694–711, 2015.

    Google Scholar 

  36. R. Johnson and T. Zhang. Effective use of word order for text categorization with convolutional neural networks. arXiv:1412.1058, 2014.https://arxiv.org/abs/1412.1058

  37. A. Karpathy, G. Toderici, S. Shetty, T. Leung, R. Sukthankar, and L. Fei-Fei. Large-scale video classification with convolutional neural networks. IEEE Conference on Computer Vision and Pattern Recognition, pp. 725–1732, 2014.

    Google Scholar 

  38. A. Karpathy, J. Johnson, and L. Fei-Fei. Stanford University Class CS321n: Convolutional neural networks for visual recognition, 2016.http://cs231n.github.io/

  39. Y. Kim. Convolutional neural networks for sentence classification. arXiv:1408.5882, 2014.

    Google Scholar 

  40. T. Kipf and M. Welling. Semi-supervised classification with graph convolutional networks. arXiv:1609.02907, 2016.https://arxiv.org/pdf/1609.02907.pdf

  41. A. Krizhevsky, I. Sutskever, and G. Hinton. Imagenet classification with deep convolutional neural networks. NIPS Conference, pp. 1097–1105. 2012.

    Google Scholar 

  42. S. Lai, L. Xu, K. Liu, and J. Zhao. Recurrent Convolutional Neural Networks for Text Classification. AAAI, pp. 2267–2273, 2015.

    Google Scholar 

  43. G. Larsson, M. Maire, and G. Shakhnarovich. Fractalnet: Ultra-deep neural networks without residuals. arXiv:1605.07648, 2016.https://arxiv.org/abs/1605.07648

  44. S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back. Face recognition: A convolutional neural-network approach. IEEE Transactions on Neural Networks, 8(1), pp. 98–113, 1997.

    CrossRef  Google Scholar 

  45. Q. Le et al. Building high-level features using large scale unsupervised learning. ICASSP, 2013.

    Google Scholar 

  46. Y. LeCun and Y. Bengio. Convolutional networks for images, speech, and time series. The Handbook of Brain Theory and Neural Networks, 3361(10), 1995.

    Google Scholar 

  47. Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11), pp. 2278–2324, 1998.

    CrossRef  Google Scholar 

  48. Y. LeCun, C. Cortes, and C. Burges. The MNIST database of handwritten digits, 1998.http://yann.lecun.com/exdb/mnist/

  49. Y. LeCun, K. Kavukcuoglu, and C. Farabet. Convolutional networks and applications in vision. IEEE International Symposium on Circuits and Systems, pp. 253–256, 2010.

    Google Scholar 

  50. H. Lee, R. Grosse, B. Ranganath, and A. Y. Ng. Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations. ICML Conference, pp. 609–616, 2009.

    Google Scholar 

  51. M. Lin, Q. Chen, and S. Yan. Network in network. arXiv:1312.4400, 2013.https://arxiv.org/abs/1312.4400

  52. A. Mahendran and A. Vedaldi. Understanding deep image representations by inverting them. IEEE Conference on Computer Vision and Pattern Recognition, pp. 5188–5196, 2015.

    Google Scholar 

  53. A. Makhzani and B. Frey. Winner-take-all autoencoders. NIPS Conference, pp. 2791–2799, 2015.

    Google Scholar 

  54. J. Masci, U. Meier, D. Ciresan, and J. Schmidhuber. Stacked convolutional auto-encoders for hierarchical feature extraction. Artificial Neural Networks and Machine Learning, pp. 52–59, 2011.

    Google Scholar 

  55. T. Mikolov, K. Chen, G. Corrado, and J. Dean. Efficient estimation of word representations in vector space. arXiv:1301.3781, 2013.https://arxiv.org/abs/1301.3781

  56. J. Y.-H. Ng, M. Hausknecht, S. Vijayanarasimhan, O. Vinyals, R. Monga, and G. Toderici. Beyond short snippets: Deep networks for video classification. IEEE Conference on Computer Vision and Pattern Recognition, pp. 4694–4702, 2015.

    Google Scholar 

  57. A. Nguyen, A. Dosovitskiy, J. Yosinski, T., Brox, and J. Clune. Synthesizing the preferred inputs for neurons in neural networks via deep generator networks. NIPS Conference, pp. 3387–3395, 2016.

    Google Scholar 

  58. M. Oquab, L. Bottou, I. Laptev, and J. Sivic. Learning and transferring mid-level image representations using convolutional neural networks. IEEE Conference on Computer Vision and Pattern Recognition, pp. 1717–1724, 2014.

    Google Scholar 

  59. O. Parkhi, A. Vedaldi, and A. Zisserman. Deep Face Recognition. BMVC, 1(3), pp. 6, 2015.

    Google Scholar 

  60. J. Pennington, R. Socher, and C. Manning. Glove: Global Vectors for Word Representation. EMNLP, pp. 1532–1543, 2014.

    Google Scholar 

  61. A. Radford, L. Metz, and S. Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv:1511.06434, 2015.https://arxiv.org/abs/1511.06434

  62. M.’ A. Ranzato, F. J. Huang, Y-L. Boureau, and Y. LeCun. Unsupervised learning of invariant feature hierarchies with applications to object recognition. Computer Vision and Pattern Recognition, pp. 1–8, 2007.

    Google Scholar 

  63. A. Razavian, H. Azizpour, J. Sullivan, and S. Carlsson. CNN features off-the-shelf: an astounding baseline for recognition. IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 806–813, 2014.

    Google Scholar 

  64. J. Redmon, S. Divvala, R. Girshick, and A. Farhadi. You only look once: Unified, real-time object detection. IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788, 2016.

    Google Scholar 

  65. H. A. Rowley, S. Baluja, and T. Kanade. Neural network-based face detection. IEEE TPAMI, 20(1), pp. 23–38, 1998.

    CrossRef  Google Scholar 

  66. A. Saxe, P. Koh, Z. Chen, M. Bhand, B. Suresh, and A. Ng. On random weights and unsupervised feature learning. ICML Confererence, pp. 1089–1096, 2011.

    Google Scholar 

  67. P. Sermanet, D. Eigen, X. Zhang, M. Mathieu, R. Fergus, and Y. LeCun. Overfeat: Integrated recognition, localization and detection using convolutional networks. arXiv:1312.6229, 2013.https://arxiv.org/abs/1312.6229

  68. E. Shelhamer, J., Long, and T. Darrell. Fully convolutional networks for semantic segmentation. IEEE TPAMI, 39(4), pp. 640–651, 2017.

    Google Scholar 

  69. P. Simard, D. Steinkraus, and J. C. Platt. Best practices for convolutional neural networks applied to visual document analysis. ICDAR, pp. 958–962, 2003.

    Google Scholar 

  70. K. Simonyan and A. Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv:1409.1556, 2014.https://arxiv.org/abs/1409.1556

  71. K. Simonyan and A. Zisserman. Two-stream convolutional networks for action recognition in videos. NIPS Conference, pp. 568–584, 2014.

    Google Scholar 

  72. K. Simonyan, A. Vedaldi, and A. Zisserman. Deep inside convolutional networks: Visualising image classification models and saliency maps. arXiv:1312.6034, 2013.

    Google Scholar 

  73. J. Springenberg, A. Dosovitskiy, T. Brox, and M. Riedmiller. Striving for simplicity: The all convolutional net. arXiv:1412.6806, 2014.https://arxiv.org/abs/1412.6806

  74. Y. Sun, D. Liang, X. Wang, and X. Tang. Deepid3: Face recognition with very deep neural networks. arXiv:1502.00873, 2013. https://arxiv.org/abs/1502.00873

  75. Y. Sun, X. Wang, and X. Tang. Deep learning face representation from predicting 10,000 classes. IEEE Conference on Computer Vision and Pattern Recognition, pp. 1891–1898, 2014.

    Google Scholar 

  76. C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich. Going deeper with convolutions. IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–9, 2015.

    Google Scholar 

  77. C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna. Rethinking the inception architecture for computer vision. IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.

    Google Scholar 

  78. C. Szegedy, S. Ioffe, V. Vanhoucke, and A. Alemi. Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning. AAAI Conference, pp. 4278–4284, 2017.

    Google Scholar 

  79. G. Taylor, R. Fergus, Y. LeCun, and C. Bregler. Convolutional learning of spatio-temporal features. European Conference on Computer Vision, pp. 140–153, 2010.

    Google Scholar 

  80. D. Tran et al. Learning spatiotemporal features with 3d convolutional networks. IEEE International Conference on Computer Vision, 2015.

    Google Scholar 

  81. R. Uijlings, A. van de Sande, T. Gevers, and M. Smeulders. Selective search for object recognition. International Journal of Computer Vision, 104(2), 2013.

    Google Scholar 

  82. A. Vedaldi and K. Lenc. Matconvnet: Convolutional neural networks for matlab. ACM International Conference on Multimedia, pp. 689–692, 2005.http://www.vlfeat.org/matconvnet/

  83. A. Veit, M. Wilber, and S. Belongie. Residual networks behave like ensembles of relatively shallow networks. NIPS Conference, pp. 550–558, 2016.

    Google Scholar 

  84. O. Vinyals, A. Toshev, S. Bengio, and D. Erhan. Show and tell: A neural image caption generator. CVPR Conference, pp. 3156–3164, 2015.

    Google Scholar 

  85. L. Wang, Y. Qiao, and X. Tang. Action recognition with trajectory-pooled deep-convolutional descriptors. IEEE Conference on Computer Vision and Pattern Recognition, pp. 4305–4314, 2015.

    Google Scholar 

  86. T. Wang, D. Wu, A. Coates, and A. Ng. End-to-end text recognition with convolutional neural networks. International Conference on Pattern Recognition, pp. 3304–3308, 2012.

    Google Scholar 

  87. S. Xie, R. Girshick, P. Dollar, Z. Tu, and K. He. Aggregated residual transformations for deep neural networks. arXiv:1611.05431, 2016.https://arxiv.org/abs/1611.05431

  88. F. Yu and V. Koltun. Multi-scale context aggregation by dilated convolutions. arXiv:1511.07122, 2015.https://arxiv.org/abs/1511.07122

  89. S. Zagoruyko and N. Komodakis. Wide residual networks. arXiv:1605.07146, 2016.https://arxiv.org/abs/1605.07146

  90. M. Zeiler, D. Krishnan, G. Taylor, and R. Fergus. Deconvolutional networks. Computer Vision and Pattern Recognition (CVPR), pp. 2528–2535, 2010.

    Google Scholar 

  91. M. Zeiler, G. Taylor, and R. Fergus. Adaptive deconvolutional networks for mid and high level feature learning. IEEE International Conference on Computer Vision (ICCV)—, pp. 2018–2025, 2011.

    Google Scholar 

  92. M. Zeiler and R. Fergus. Visualizing and understanding convolutional networks. European Conference on Computer Vision, Springer, pp. 818–833, 2013.

    Google Scholar 

  93. X. Zhang, J. Zhao, and Y. LeCun. Character-level convolutional networks for text classification. NIPS Conference, pp. 649–657, 2015.

    Google Scholar 

  94. C. Zitnick and P. Dollar. Edge Boxes: Locating object proposals from edges. ECCV, pp. 391–405, 2014.

    Google Scholar 

  95. http://caffe.berkeleyvision.org/

  96. http://torch.ch/

  97. http://deeplearning.net/software/theano/

  98. https://www.tensorflow.org/

  99. https://keras.io/

  100. https://lasagne.readthedocs.io/en/latest/

  101. http://www.image-net.org/

  102. http://www.image-net.org/challenges/LSVRC/

  103. https://www.cs.toronto.edu/~kriz/cifar.html

  104. http://code.google.com/p/cuda-convnet/

  105. http://caffe.berkeleyvision.org/gathered/examples/feature_extraction.html

  106. https://github.com/caffe2/caffe2/wiki/Model-Zoo

  107. http://horatio.cs.nyu.edu/mit/tiny/data/

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Aggarwal, C.C. (2018). Convolutional Neural Networks. In: Neural Networks and Deep Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-94463-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94463-0_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94462-3

  • Online ISBN: 978-3-319-94463-0

  • eBook Packages: Computer ScienceComputer Science (R0)