Abstract
This paper aims to introduce the proposal of replacing the usual pooling functions by the Choquet integral in Deep Learning Networks. The Choquet integral is an aggregation function studied and applied in several areas, as, e.g., in classification problems. Its importance is related to the fact that it considers the relationship between the data to be aggregated by means of a fuzzy measure, unlike other aggregation functions such as the arithmetic mean and the maximum. The idea of this paper is to use the Choquet integral to reduce the size of an image, obtaining an abstract form of representation, that is, reducing the perception of the network corresponding to small changes in the image. The use of this aggregation function in the place of the max-pooling and mean-pooling functions of Convolutional Neural Networks presented promising results. This assertion is based on the Normalized Cross-Correlation and Structural Content quality measures applied to the original images and resulting images. It is important to emphasize that this preliminary study of Choquet integral as a pool layer has not yet been implemented on Convolutional Neural Networks until the present moment.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Agarap, A.F.: An Architecture Combining Convolutional Neural Network (CNN) and Support Vector Machine (SVM) for Image Classification. Adamson University, Manila (2017)
Ahmed, A., Yu, K., Xu, W., Gong, Y., Xing, E.: Training hierarchical feed-forward visual recognition models using transfer learning from pseudo-tasks. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5304, pp. 69–82. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88690-7_6
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners, vol. 221. Springer, Berlin/Heidelberg (2007). https://doi.org/10.1007/978-3-540-73721-6
Boureau, Y.L., Ponce, J., Lecun, Y.: A theoretical analysis of feature pooling in visual recognition. In: Proceedings of the 27th International Conference on Machine Learning (ICML-2010), Haifa, Israel, pp. 111–118 (2010)
Choquet, G.: Theory of capacities. In: Annales de l’institut Fourier, Grenoble, France, vol. 5, pp. 131–295 (1954)
Deepika, J., Vishvanathan, S., KP, S.: Image classification using convolutional neural networks. Int. J. Sci. Eng. Res. 5(6), 1661–1668 (2014)
Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: imageNet: a large-scale hierarchical image database. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2009), Miami, Florida, pp. 248–255. IEEE (2009)
Eskicioglu, A.M., Fisher, P.S.: Image quality measures and their performance. IEEE Trans. Commun. 43(12), 2959–2965 (1995)
Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation functions: means. Inf. Sci. 181(1), 1–22 (2011)
Han, Y., Kim, J., Lee, K., Han, Y., Kim, J., Lee, K.: Deep convolutional neural networks for predominant instrument recognition in polyphonic music. IEEE/ACM Trans. Audio, Speech Lang. Process. (TASLP) 25(1), 208–221 (2017)
Hodges, J.L., Lehmann, E.L.: Rank methods for combination of independent experiments in analysis of variance. Ann. Math. Stat. 33(2), 482–497 (1962)
Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep con-volutional neural networks. In: Advances in Neural Information Processing Systems (NIPS), Stateline, NV, pp. 1097–1105 (2012)
Lecun, Y., Huang, F.J., Bottou, L.: Learning Methods for generic object recognition with invariance to pose and lighting. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2004), Washington, D.C., USA, vol. 2, pp. II–104. IEEE (2004)
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Mesiar, R., Kolesárová, A., Bustince, H.: Preaggregation functions: construction and an application. IEEE Trans. Fuzzy Syst. 24(2), 260–272 (2016)
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Asiain, M.J., Elkano, M., Bustince, H.: CC-integrals: choquet-like copula-based aggregation functions and its application in fuzzy rule-based classification systems. Knowl.-Based Syst. 119, 32–43 (2017)
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Bustince, H., Mesiar, R.: CF-integrals: a new family of pre-aggregation functions with application to fuzzy rule-based classification systems. Inf. Sci. 435, 94–110 (2018)
Mishra, A., Alahari, K., Jawahar, C.V.: Scene text recognition using higher order language priors. In: 23rd British Machine Vision Conference, BMVC 2012, Paris, France (2012)
Pagola, M., Forcen, J.I., Barrenechea, E., Lopez-Molina, C., Bustince, H.: Use of OWA operators for feature aggregation in image classification. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2017), Naples, Italy, pp. 1–6. IEEE (2017)
Saxe, A.M., Koh, P.W., Chen, Z., Bhand, M., Suresh, B., Ng, A.Y.: On random weights and unsupervised feature learning. In: Proceedings of the 28th International Conference on Machine Learning (ICML-2011), Bellevue, Washington, USA, pp. 1089–1096. Bellevue, Washington, USA (2011)
Scherer, D., Müller, A., Behnke, S.: Evaluation of pooling operations in convolutional architectures for object recognition. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010. LNCS, vol. 6354, pp. 92–101. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15825-4_10
Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics Bull. 1(6), 80–83 (1945)
Wu, H., Gu, X.: Max-pooling dropout for regularization of convolutional neural networks. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds.) ICONIP 2015. LNCS, vol. 9489, pp. 46–54. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26532-2_6
Wu, J.: Introduction to Convolutional Neural Networks. National Key Lab for Novel Software Technology. Nanjing University, China (2017)
Yu, D., Wang, H., Chen, P., Wei, Z.: Mixed pooling for convolutional neural networks. International Conference on Rough Sets and Knowledge Technology, pp. 364–375. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11740-9_34
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Dias, C.A. et al. (2018). Using the Choquet Integral in the Pooling Layer in Deep Learning Networks. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-95312-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95311-3
Online ISBN: 978-3-319-95312-0
eBook Packages: Computer ScienceComputer Science (R0)