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A Note on the k-NN Density Estimate

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Intelligent Data Engineering and Automated Learning – IDEAL 2016 (IDEAL 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9937))

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Abstract

k-NN (k Nearest Neighbour) density estimate as a nonparametric estimation method is widely used in machine learning or data analysis. The convergence problem of k-NN approach has been intensively investigated. In particular, the equivalence of convergence in weak or strong sense (i.e. in probability sense or in almost surely sense) has been respectively developed. In this note, we will show that the k-NN estimator converges in probability is equivalent to converge in the \(L^2\) sense. Moreover, some relevant asymptotic results about the expectations of k-NN estimator will be established.

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Acknowledgements

The authors acknowledge the financial support by the National NSF of China under Grant No. 61472343, as well as the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-2015KF-05, Beihang University.

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Authors and Affiliations

  1. School of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Jie Ding

  2. State Key Laboratory of Software Development Environment, Beihang University, Beijing, China

    Jie Ding

  3. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China

    Jie Ding

  4. School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072, China

    Xinshan Zhu

Authors
  1. Jie Ding
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  2. Xinshan Zhu
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Corresponding author

Correspondence to Jie Ding .

Editor information

Editors and Affiliations

  1. University of Manchester, Manchester, United Kingdom

    Hujun Yin

  2. Nanjing University, Nanjing, China

    Yang Gao

  3. Yangzhou University, Yangzhou, Jiangsu, China

    Bin Li

  4. Aeronautics and Astronautics, Nanjing University Aeronautics and Astronautics, Nanjing, China

    Daoqiang Zhang

  5. Nanjing Normal University, Nanjing, China

    Ming Yang

  6. Yangzhou University, Yangzhou, Jiangsu, China

    Yun Li

  7. Ostfalia University of Applied Sciences, Wolfenbüttel, Germany

    Frank Klawonn

  8. University of Seville, Seville, Spain

    Antonio J. Tallón-Ballesteros

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© 2016 Springer International Publishing AG

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Ding, J., Zhu, X. (2016). A Note on the k-NN Density Estimate. In: Yin, H., et al. Intelligent Data Engineering and Automated Learning – IDEAL 2016. IDEAL 2016. Lecture Notes in Computer Science(), vol 9937. Springer, Cham. https://doi.org/10.1007/978-3-319-46257-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-46257-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46256-1

  • Online ISBN: 978-3-319-46257-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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