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Full Rotation Hyper-ellipsoid Multivariate Adaptive Bandwidth Kernel Density Estimator

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Artificial Intelligence Research (SACAIR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1551))

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Abstract

Adaptive bandwidth kernel density estimators (AB-KDEs) have received attention from the academic community due to an analytical promise of increased performance over classical estimators. However, the field is fragmented, and there exists no comprehensive comparison of the existing state-of-the-art AB-KDEs. We provide a comparison of some state-of-the-art and classical AB-KDE methods as well as a computational framework. We also present a novel implementation of a full principal axes rotation hyper-ellipsoid variant of the k-Nearest Neighbours algorithm and a Gaussian extension to K-NN. The extensive experimental results show the fixed bandwidth rule-of-thumb methods achieve satisfactory results. Further, the balloon estimators are shown to be superior in the higher dimensional spaces, with higher modes or data on non-linear manifolds. The sample point estimators show utility when data are scarce in low dimensions. The empirical results show that our full rotation hyper-ellipsoid estimator and our Gaussian K-NN are state-of-the-art and will have a significant positive impact on data analysis algorithms. Especially algorithms which depend upon underlying density estimates on “complex” higher-dimensional data.

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Author information

Authors and Affiliations

  1. Institute for Intelligent Systems, University of Johannesburg, Johannesburg, South Africa

    Terence L. van Zyl

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  1. Terence L. van Zyl
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Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Edgar Jembere

  2. University of Pretoria, Pretoria, South Africa

    Aurona J. Gerber

  3. University of KwaZulu-Natal, Durban, South Africa

    Serestina Viriri

  4. University of KwaZulu-Natal, Durban, South Africa

    Anban Pillay

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van Zyl, T.L. (2022). Full Rotation Hyper-ellipsoid Multivariate Adaptive Bandwidth Kernel Density Estimator. In: Jembere, E., Gerber, A.J., Viriri, S., Pillay, A. (eds) Artificial Intelligence Research. SACAIR 2021. Communications in Computer and Information Science, vol 1551. Springer, Cham. https://doi.org/10.1007/978-3-030-95070-5_19

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  • DOI: https://doi.org/10.1007/978-3-030-95070-5_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95069-9

  • Online ISBN: 978-3-030-95070-5

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