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Interpretable Convolutional Neural Networks Using a Rule-Based Framework for Classification

  • Zhen XiEmail author
  • George Panoutsos
Chapter
  • 33 Downloads
Part of the Studies in Computational Intelligence book series (SCI, volume 864)

Abstract

A convolutional neural network (CNN) learning structure is proposed, with added interpretability-oriented layers, in the form of Fuzzy Logic-based rules. This is achieved by creating a classification layer based on a Neural Fuzzy classifier, and integrating it into the overall learning mechanism within the deep learning structure. Using this new structure, one can extract linguistic Fuzzy Logic-based rules from the deep learning structure directly, and link this information to input features, which enhances the interpretability of the overall system. The classification layer is realised via a Radial Basis Function (RBF) Neural-Network, that is a direct equivalent of a class of Fuzzy Logic-based systems. In this work, the development of the RBF neural-fuzzy system and its integration into the deep-learning CNN is presented. The proposed hybrid CNN RBF-NF structure can form a fundamental building block, towards building more complex deep-learning structures with Fuzzy Logic-based interpretability. Using simulation results on benchmark data (MNIST handwriting digits and MNIST Fashion) we show that the proposed learning structure maintains a good level of forecasting/prediction accuracy compared to CNN deep learning structures. Crucially, we also demonstrate in both cases the resulting interpretability, in the form of linguistic rules that link the classification decisions to the input feature space.

Keywords

Deep learning Convolutional neural networks Fuzzy logic Interpretable machine learning 

References

  1. 1.
    R. Schaprie, Computer Science 511 Theoretical Machine Learning (Computer Science Department, Princeton University, Princeton, 2008)Google Scholar
  2. 2.
    M.I. Jordan, T.M. Mitchell, Machine learning: trends, perspectives, and prospects. Science 349(6245), 255–260 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521(7553), 436–444 (2015)CrossRefGoogle Scholar
  4. 4.
    J. Gong, M.D. Goldman, J. Lach, Deep motion: a deep convolutional neural network on inertial body sensors for gait assessment in multiple sclerosis, in 2016 IEEE Wireless Health, WH 2016 (2016), pp 164–171Google Scholar
  5. 5.
    T. Segreto, A. Caggiano, S. Karam, R. Teti, Vibration sensor monitoring of nickel-titanium alloy turning for machinability evaluation. Sensors (Switzerland) 17(12) (2017)Google Scholar
  6. 6.
    C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, A. Rabinovich, Going deeper with convolutions, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2015), pp 1–9Google Scholar
  7. 7.
    A. Krizhevsky, I. Sutskever, G.E. Hinton, Imagenet classification with deep convolutional neural networks, in Advances in Neural Information Processing Systems 25, ed. by F. Pereira, C.J.C. Burges, L. Bottou, K.Q. Weinberger (Curran Associates, Inc., 2012), pp 1097–1105Google Scholar
  8. 8.
    Y. LeCun, L. Bottou, Y. Bengio, P. Haffner, Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  9. 9.
    J. Deng, W. Dong, R. Socher, L. Li, ImageNet: A large-scale hierarchical image database, in 2009 IEEE Conference on Computer Vision and Pattern Recognition (2009), pp. 248–255Google Scholar
  10. 10.
    K. He, X. Zhang, S. Ren, J. Sun, Deep Residual Learning for Image Recognition (2015). CoRR abs/1512.03385Google Scholar
  11. 11.
    K. Simonyan, A. Zisserman, Very deep convolutional networks for large-scale image recognition. CoRR (2014)Google Scholar
  12. 12.
    G. Panoutsos, M. Mahfouf, A neural-fuzzy modelling framework based on granular computing: concepts and applications. Fuzzy Sets Syst. 161(21), 2808–2830 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    G. Panoutsos, M. Mahfouf, G.H. Mills, B.H. Brown, A generic framework for enhancing the interpretability of granular computing-based information, in 2010 5th IEEE International Conference Intelligent Systems. IEEE (2010), pp. 19–24Google Scholar
  14. 14.
    R.P. Paiva, A. Dourado, Interpretability and learning in neuro-fuzzy systems. Fuzzy Sets Syst. 147(1), 17–38 (2004)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Muniategui, B. Hériz, L. Eciolaza, M. Ayuso, A. Iturrioz, I. Quintana, P. Álvarez, Spot welding monitoring system based on fuzzy classification and deep learning, in 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2017), pp. 1–6Google Scholar
  16. 16.
    Y. Deng, Z. Ren, Y. Kong, F. Bao, Q. Dai, A hierarchical fused fuzzy deep neural network for data classification. IEEE Tran. Fuzzy Syst. 25(4), 1006–1012 (2017)CrossRefGoogle Scholar
  17. 17.
    D.S. Broomhead, D. Lowe, Radial Basis Functions, Multi-variable Functional Interpolation and Adaptive Networks Technical report, Royal Signals and Radar Establishment Malvern (United Kingdom) (1988)Google Scholar
  18. 18.
    K. Muller, S. Mika, G. Ratsch, K. Tsuda, B. Scholkopf, An introduction to Kernel-based learning algorithms. IEEE Trans. Neural Netw. 12(2), 181–201 (2001)CrossRefGoogle Scholar
  19. 19.
    M.Y. Chen, D.A. Linkens, A systematic neuro-fuzzy modeling framework with application to material property prediction. IEEE Trans. Syst. Man Cybern. B Cybern. 31(5), 781–90 (2001)CrossRefGoogle Scholar
  20. 20.
    X. Glorot, A. Bordes, Y. Bengio, Deep sparse rectifier neural networks, in Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics (2011), pp 315–323Google Scholar
  21. 21.
    S. Ioffe, C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift (2015). CoRR abs/1502.03167Google Scholar
  22. 22.
    T. Schaul, I. Antonoglou, D. Silver, Unit Tests for Stochastic Optimization (2013). arXiv:13126055 [cs] 1312.6055
  23. 23.
    Y. Bengio, N. Boulanger-Lewandowski, R. Pascanu, Advances in optimizing recurrent networks, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (2013), pp. 8624–8628Google Scholar
  24. 24.
    J. Duchi, E. Hazan, Y. Singer, Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)Google Scholar
  25. 25.
    N. Srivastava, G.E. Hinton, A. Krizhevsky, I. Sutskever, R. Salakhutdinov, Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)MathSciNetzbMATHGoogle Scholar
  26. 26.
    S. Al-sharhan, F. Karray, W. Gueaieb, O. Basir, Fuzzy entropy: a brief survey, in 10th IEEE International Conference on Fuzzy Systems (Cat. No.01CH37297), vol. 3, vol. 2 (2001), pp. 1135–1139Google Scholar
  27. 27.
    M.D. Zeiler, ADADELTA: An Adaptive Learning Rate Method (2012). CoRR abs/1212.5701Google Scholar
  28. 28.
    D. Cireşan, U. Meier, J. Schmidhuber, Multi-column Deep Neural Networks for Image Classification (2012). arXiv:12022745 [cs] 1202.2745
  29. 29.
    H. Xiao, K. Rasul, R. Vollgraf, Fashion-MNIST: A Novel Image Dataset for Benchmarking Machine Learning Algorithms (2017). CoRR abs/1708.07747, 1708.07747Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Automatic Control and Systems EngineeringUniversity of SheffieldSheffieldUK

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