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Spectral Clustering Algorithm for the Allometric Extension Model

Author

Listed:
  • Kohei Kawamoto

    (Kyushu University)

  • Yuichi Goto

    (Kyushu University)

  • Koji Tsukuda

    (Kyushu University)

Abstract

The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. When investigating the theoretical properties of the spectral clustering algorithm, existing studies have tended to invoke the assumption of conditional homoscedasticity. However, this assumption is restrictive and, in practice, often unrealistic. Therefore, in this paper, we consider the allometric extension model in which the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide. We derive a non-asymptotic bound for the error probability of the spectral clustering algorithm under this allometric extension model. As a byproduct of this result, we demonstrate that the clustering method is consistent in high-dimensional settings.

Suggested Citation

  • Kohei Kawamoto & Yuichi Goto & Koji Tsukuda, 2025. "Spectral Clustering Algorithm for the Allometric Extension Model," Statistical Papers, Springer, vol. 66(3), pages 1-32, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01680-3
    DOI: 10.1007/s00362-025-01680-3
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    References listed on IDEAS

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    1. Kurata, Hiroshi & Hoshino, Takahiro & Fujikoshi, Yasunori, 2008. "Allometric extension model for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1985-1998, October.
    2. Stefania Bartoletti & Bernard D. Flury & Daan G. Nel, 1999. "Allometric Extension," Biometrics, The International Biometric Society, vol. 55(4), pages 1210-1214, December.
    3. Borysov, Petro & Hannig, Jan & Marron, J.S., 2014. "Asymptotics of hierarchical clustering for growing dimension," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 465-479.
    4. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
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