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A fresh look at mean-shift based modal clustering

Author

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  • Jose Ameijeiras-Alonso

    (Universidade de Santiago de Compostela)

  • Jochen Einbeck

    (Durham University
    Durham University)

Abstract

Modal clustering is an unsupervised learning technique where cluster centers are identified as the local maxima of nonparametric probability density estimates. A natural algorithmic engine for the computation of these maxima is the mean shift procedure, which is essentially an iteratively computed chain of local means. We revisit this technique, focusing on its link to kernel density gradient estimation, in this course proposing a novel concept for bandwidth selection based on the concept of a critical bandwidth. Furthermore, in the one-dimensional case, an inverse version of the mean shift is developed to provide a novel approach for the estimation of antimodes, which is then used to identify cluster boundaries. A simulation study is provided which assesses, in the univariate case, the classification accuracy of the mean-shift based clustering approach. Three (univariate and multivariate) examples from the fields of philately, engineering, and imaging, illustrate how modal clusterings identified through mean shift based methods relate directly and naturally to physical properties of the data-generating system. Solutions are proposed to deal computationally efficiently with large data sets.

Suggested Citation

  • Jose Ameijeiras-Alonso & Jochen Einbeck, 2024. "A fresh look at mean-shift based modal clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(4), pages 1067-1095, December.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:4:d:10.1007_s11634-023-00575-1
    DOI: 10.1007/s11634-023-00575-1
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    References listed on IDEAS

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    1. Azzalini, Adelchi & Menardi, Giovanna, 2014. "Clustering via Nonparametric Density Estimation: The R Package pdfCluster," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i11).
    2. Christopher R. Genovese & Marco Perone-Pacifico & Isabella Verdinelli & Larry Wasserman, 2016. "Non-parametric inference for density modes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 99-126, January.
    3. Hennig, Christian & Christlieb, Norbert, 2002. "Validating visual clusters in large datasets: fixed point clusters of spectral features," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 723-739, October.
    4. Alessandro Casa & Luca Scrucca & Giovanna Menardi, 2021. "Better than the best? Answers via model ensemble in density-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 599-623, September.
    5. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
    6. Giovanna Menardi, 2016. "A Review on Modal Clustering," International Statistical Review, International Statistical Institute, vol. 84(3), pages 413-433, December.
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