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Projection pursuit via kernel mean embeddings

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  • Warth, Oliver
  • Dümbgen, Lutz

Abstract

Detecting and visualizing interesting structures in high-dimensional data is a ubiquitous challenge. If one aims for linear projections onto low-dimensional spaces, a well-known problematic phenomenon is the Diaconis–Freedman effect: under mild conditions, most projections do not reveal interesting structures but look like scale mixtures of spherically symmetric Gaussian distributions. We present a method which combines global search strategies and local projection pursuit via maximizing the maximum mean discrepancy (MMD) between the empirical distribution of the projected data and a data-driven Gaussian mixture distribution. Here, MMD is based on kernel mean embeddings with Gaussian kernels.

Suggested Citation

  • Warth, Oliver & Dümbgen, Lutz, 2026. "Projection pursuit via kernel mean embeddings," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001290
    DOI: 10.1016/j.jmva.2025.105534
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    References listed on IDEAS

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    1. David E. Tyler & Frank Critchley & Lutz Dümbgen & Hannu Oja, 2009. "Invariant co‐ordinate selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 549-592, June.
    2. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    3. Kampstra, Peter, 2008. "Beanplot: A Boxplot Alternative for Visual Comparison of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(c01).
    4. Lutz Dümbgen & Katrin Gysel & Fabrice Perler, 2023. "Refining Invariant Coordinate Selection via Local Projection Pursuit," Springer Books, in: Mengxi Yi & Klaus Nordhausen (ed.), Robust and Multivariate Statistical Methods, pages 121-136, Springer.
    5. Nicola Loperfido, 2019. "Finite mixtures, projection pursuit and tensor rank: a triangulation," 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. 13(1), pages 145-173, March.
    6. Guy P. Nason, 2001. "Robust projection indices," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 551-567.
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