Application of Learned OWA Operators in Pooling and Channel Aggregation Layers in Convolutional Neural Networks

  • Leonam R. S. Miranda UFMG
  • Frederico G. Guimarães UFMG


Promising results have been obtained in recent years when using OWA operators to aggregate data within CNNs pool layers, training their weights, instead of using the more usual operators (max and mean). OWA operators were also used to learn channel wise information from a certain layer, and the newly generated information is used to complement the input data for the following layer. The purpose of this article is to analyze and combine the two mentioned ideas. In addition to using the channel wise information generated by trainable OWA operators to complement the input data, replacement will also be analyzed. Several tests have been done to evaluate the performance change when applying OWA operators to classify images using VGG13 model.


Anderson, D. T., Scott, G. J., Islam, M. A., Murray, B., and Marcum, R. (2018). Fuzzy choquet integration of deep convolutional neural networks for remote sensing. In Computational Intelligence for Pattern Recognition, pages 1-28. Springer.

Boureau, Y.-L., Ponce, J., and LeCun, Y. (2010). A theoretical analysis of feature pooling in visual recognition. In Proceedings of the 27th international conference on machine learning (ICML-10), pages 111-118.

Chollet, F. et al. (2015). Keras.

Dias, C. A., Bueno, J., Borges, E. N., Botelho, S. S., Dimuro, G. P., Lucca, G., Fernandéz, J., Bustince, H., and Drews Junior, P. L. J. (2018). Using the choquet integral in the pooling layer in deep learning networks. In North american fuzzy information processing society annual conference, pages 144-154. Springer.

Dominguez-Catena, I., Paternain, D., and Galar, M. (2020). Additional feature layers from ordered aggregations for deep neural networks. In 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1-8. IEEE.

Dominguez-Catena, I., Paternain, D., and Galar, M. (2021). A study of owa operators learned in convolutional neural networks. Applied Sciences, 11(16):7195.

Forcen, J. I., Pagola, M., Barrenechea, E., and Bustince, H. (2020). Learning ordered pooling weights in image classification. Neurocomputing, 411:45-53.

Grabisch, M., Marichal, J.-L., Mesiar, R., and Pap, E. (2009). Aggregation functions, volume 127. Cambridge University Press.

He, K., Zhang, X., Ren, S., and Sun, J. (2015). Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pages 1026-1034.

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

Herrera, F. and Martínez, L. (2001). A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 31(2):227-234.

Jie, H. J. and Wanda, P. (2020). Runpool: A dynamic pooling layer for convolution neural network. Int. J. Comput. Intell. Syst., 13(1):66-76.

Keller, J. M., Liu, D., and Fogel, D. B. (2016). Fundamentals of computational intelligence: neural networks, fuzzy systems, and evolutionary computation. John Wiley & Sons.

Krizhevsky, A., Hinton, G., et al. (2009). Learning multiple layers of features from tiny images.

Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012). Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25.

Liu, S. and Deng, W. (2015). Very deep convolutional neural network based image classification using small training sample size. In 2015 3rd IAPR Asian conference on pattern recognition (ACPR), pages 730-734. IEEE.

Pagola, M., Forcen, J. I., Barrenechea, E., Lopez-Molina, C., and Bustince, H. (2017). Use of owa operators for feature aggregation in image classification. In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1-6. IEEE.

Price, S. R., Price, S. R., and Anderson, D. T. (2019). Introducing fuzzy layers for deep learning. In 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1-6. IEEE.

Rudin, L. I., Osher, S., and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60(1-4):259-268.

Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., et al. (2015). Imagenet large scale visual recognition challenge. International journal of computer vision, 115(3):211-252.

Scott, G. J., Marcum, R. A., Davis, C. H., and Nivin, T. W. (2017). Fusion of deep convolutional neural networks for land cover classification of high-resolution imagery. IEEE Geoscience and Remote Sensing Letters, 14(9):1638-1642.

Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3):379-423.

Simonyan, K. and Zisserman, A. (2014). Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556.

Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on systems, Man, and Cybernetics, 18(1):183- 190.

Yu, D., Wang, H., Chen, P., and Wei, Z. (2014). Mixed pooling for convolutional neural networks. In International conference on rough sets and knowledge technology, pages 364-375. Springer.

Zhou, S.-M., Chiclana, F., John, R. I., and Garibaldi, J. M. (2008). Type-1 owa operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers. Fuzzy Sets and Systems, 159(24):3281-3296.
MIRANDA, Leonam R. S.; GUIMARÃES, Frederico G.. Application of Learned OWA Operators in Pooling and Channel Aggregation Layers in Convolutional Neural Networks. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 19. , 2022, Campinas/SP. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 567-578. ISSN 2763-9061. DOI: