Abstract
Artificial neural network (ANN) is one of the most common methods for data regression. However, existing ANN based methods focus on fitting data with explicit relationships, where the output y can be explicitly expressed by the inputs x in the form of \(y = f(x)\). In contrast, implicit relationships (i.e., \(f(x,y)=0\)) are more expressive in that they can concisely present complex closed surfaces and mathematical functions with multiple outputs. However, so far, little effort has been made on applying ANN to fit data with implicit relationships of variables. In this paper, for the first time, we propose an implicit neural network (INN) for implicit data regression. In this framework, an evolutionary implicit neural network (EINN) module is proposed, which is trained by the regression data to capture the implicit relationships among variables. Then, an explicit-implicit cooperate (EIC) mechanism is proposed based on the EINN component to train an explicit ANN model to predict the outputs of new unseen inputs. The proposed framework is tested on eight benchmark problems and the experimental results have demonstrated the efficacy of the proposed method.
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Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Mohamed, N.A., Arshad, H.: State-of-the-art in artificial neural network applications: a survey. Heliyon 4(11), e00938 (2018)
Sateesh Babu, G., Zhao, P., Li, X.-L.: Deep convolutional neural network based regression approach for estimation of remaining useful life. In: Navathe, S.B., Wu, W., Shekhar, S., Du, X., Wang, X.S., Xiong, H. (eds.) DASFAA 2016. LNCS, vol. 9642, pp. 214–228. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32025-0_14
Besseris, G.J.: Taguchi-generalized regression neural network micro-screening for physical and sensory characteristics of bread. Heliyon 4(3), e00551 (2018)
Chen, Y., Zhong, J., Tan, M.: Comprehensive learning gene expression programming for automatic implicit equation discovery. In: Shi, Y., et al. (eds.) ICCS 2018. LNCS, vol. 10860, pp. 114–128. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93698-7_9
Li, H.z., Guo, S., Li, C.j., Sun, J.q.: A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl.-Based Syst. 37, 378–387 (2013)
O’Malley, T., et al.: Keras tuner (2019). https://github.com/keras-team/keras-tuner
Schmidt, M., Lipson, H.: Symbolic regression of implicit equations. In: Riolo, R., O’Reilly, U.M., McConaghy, T. (eds.) Genetic Programming Theory and Practice VII. GEVO, pp. 73–85. Springer, Boston (2010). https://doi.org/10.1007/978-1-4419-1626-6_5
Shi, B., Bai, X., Liu, W., Wang, J.: Deep regression for face alignment. arXiv preprint arXiv:1409.5230 (2014)
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)
Zhong, J., Yang, J., Chen, Y., Liu, W.L., Feng, L.: Mining implicit equations from data using gene expression programming. IEEE Trans. Emerg. Top. Comput. (2021). https://doi.org/10.1109/TETC.2021.3068651
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 62076098), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No.: 2017ZT07X183), the Guangdong Provincial Key Laboratory (Grant No. 2020B121201001), and the Stable Support Plan Program of Shenzhen Natural Science Fund (Grant No. 20200925154942002).
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Miao, Z., Zhong, J., Yang, P., Wang, S., Liu, D. (2021). Implicit Neural Network for Implicit Data Regression Problems. In: Mantoro, T., Lee, M., Ayu, M.A., Wong, K.W., Hidayanto, A.N. (eds) Neural Information Processing. ICONIP 2021. Communications in Computer and Information Science, vol 1516. Springer, Cham. https://doi.org/10.1007/978-3-030-92307-5_22
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DOI: https://doi.org/10.1007/978-3-030-92307-5_22
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