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Geometric goodness of fit measure to detect patterns in data point clouds

Author

Listed:
  • Alberto J. Hernández

    (Escuela de Matemática, Universidad de Costa Rica)

  • Maikol Solís

    (Escuela de Matemática, Universidad de Costa Rica)

Abstract

In this work, we derive a geometric goodness-of-fit index similar to $$R^{2}$$ R 2 using geometric data analysis techniques. We build the alpha shape complex from the data-cloud projected onto each variable and estimate the area of the complex and its domain. We create an index that measures the difference of area between the alpha shape and the smallest squared window of observation containing the data. By applying ideas similar to those found in the closest neighbor distribution and empty space distribution functions, we can establish when the characterizing geometric features of the point set emerge. This allows for a more precise application for our index. We provide some examples with anomalous patterns to show how our algorithm performs.

Suggested Citation

  • Alberto J. Hernández & Maikol Solís, 2023. "Geometric goodness of fit measure to detect patterns in data point clouds," Computational Statistics, Springer, vol. 38(3), pages 1231-1253, September.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:3:d:10.1007_s00180-022-01244-1
    DOI: 10.1007/s00180-022-01244-1
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    References listed on IDEAS

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    1. Press, S. James & Zellner, Arnold, 1978. "Posterior distribution for the multiple correlation coefficient with fixed regressors," Journal of Econometrics, Elsevier, vol. 8(3), pages 307-321, December.
    2. A. P. Barten, 1962. "Note on unbiased estimation of the squared multiple correlation coefficient," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 16(2), pages 151-164, June.
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