Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Compositional data analysis by the square-root transformation: Application to NBA USG% data

  • Jeseok Lee (Department of Statistics, Kyungpook National University) ;
  • Byungwon Kim (Department of Statistics, Kyungpook National University)
  • Received : 2023.10.21
  • Accepted : 2024.02.05
  • Published : 2024.05.31
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Abstract

Compositional data refers to data where the sum of the values of the components is a constant, hence the sample space is defined as a simplex making it impossible to apply statistical methods developed in the usual Euclidean vector space. A natural approach to overcome this restriction is to consider an appropriate transformation which moves the sample space onto the Euclidean space, and log-ratio typed transformations, such as the additive log-ratio (ALR), the centered log-ratio (CLR) and the isometric log-ratio (ILR) transformations, have been mostly conducted. However, in scenarios with sparsity, where certain components take on exact zero values, these log-ratio type transformations may not be effective. In this work, we mainly suggest an alternative transformation, that is the square-root transformation which moves the original sample space onto the directional space. We compare the square-root transformation with the log-ratio typed transformation by the simulation study and the real data example. In the real data example, we applied both types of transformations to the USG% data obtained from NBA, and used a density based clustering method, DBSCAN (density-based spatial clustering of applications with noise), to show the result.

Keywords

Acknowledgement

This research was supported by Kyungpook National University Research Fund, 2021.

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