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A Complete Efficient FFT-Based Algorithm for Nonparametric Kernel Density Estimation

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Artificial Intelligence and Soft Computing (ICAISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10246))

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Abstract

Multivariate kernel density estimation (KDE) is a very important statistical technique in exploratory data analysis. Research on high performance KDE is still an open research problem. One of the most elegant and efficient approach utilizes the Fast Fourier Transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In the paper we propose a crucial improvement to this algorithm which results in relaxing the above mentioned limitation. Numerical simulation study demonstrates good properties of the new solution.

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Author information

Authors and Affiliations

  1. Computer Center, University of Zielona Góra, Zielona Góra, Poland

    Jarosław Gramacki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Artur Gramacki

Authors
  1. Jarosław Gramacki
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  2. Artur Gramacki
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Corresponding author

Correspondence to Artur Gramacki .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Gramacki, J., Gramacki, A. (2017). A Complete Efficient FFT-Based Algorithm for Nonparametric Kernel Density Estimation. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2017. Lecture Notes in Computer Science(), vol 10246. Springer, Cham. https://doi.org/10.1007/978-3-319-59060-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-59060-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59059-2

  • Online ISBN: 978-3-319-59060-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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