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A Discrete Cosine Transform Based Evolutionary Algorithm and Its Application for Symbolic Regression

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Book cover Intelligent Computing (CompCom 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 997))

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Abstract

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies, the energy-compaction property of which makes itself very suitable for symbolic regression problems with noisy data samples. In this paper, we propose a DCT based genetic programming (DCT-GP) for symbolic regression or other optimization problems with noisy experimental observations. Firstly, a sequence of experimental samples was changed from time domain into frequency domain with DCT. Secondly, the boundary between the low frequency components and high frequency components was decided, by which most of the noise inserted into the sample data can be discarded. The experimental sample sequence was rebuilt with the low frequency components. Finally, the new obtained samples were looked on as another fitness function and were used to direct the evolutionary procedure of GP. In this way, DCT was integrated into the GP algorithm. The major advantage of the DCT-GP algorithm is that, on the one hand, it can deal with the regression problem with noisy data samples and obtain accurate solutions. On the other hand, if the sample scale is very small, it can deal with the over-fitting problem in the regression progress and can avoid losing of structure information when the available samples were departed into training set and validating set. The performance of the proposed DCT-GP algorithm with several regression problems indicates that the proposed algorithm can find the solution more efficiently and effectively than traditional sample-partitioning based GP algorithms.

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Acknowledgements

We are grateful to the anonymous referees for their invaluable suggestions to improve the paper. This work is financially supported by The National Key Research and Development Program of China (No. 2018YFC0704304).

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Authors and Affiliations

  1. Institute of Information Engineering, Chinese Academy of Science, Beijing, 100093, China

    Quanchao Liu & Yue Hu

  2. University of Chinese Academy of Science, Beijing, 100049, China

    Yue Hu

Authors
  1. Quanchao Liu
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  2. Yue Hu
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Corresponding author

Correspondence to Quanchao Liu .

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Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

  2. The Science and Information SAI Organization, Bradford, West Yorkshire, UK

    Rahul Bhatia

  3. The Science and Information SAI Organization, Bradford, West Yorkshire, UK

    Supriya Kapoor

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Liu, Q., Hu, Y. (2019). A Discrete Cosine Transform Based Evolutionary Algorithm and Its Application for Symbolic Regression. In: Arai, K., Bhatia, R., Kapoor, S. (eds) Intelligent Computing. CompCom 2019. Advances in Intelligent Systems and Computing, vol 997. Springer, Cham. https://doi.org/10.1007/978-3-030-22871-2_30

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