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L p -Norm for Compositional Data: Exploring the CoDa L 1 -Norm in Penalised Regression

Author

Listed:
  • Jordi Saperas-Riera

    (Department of Computer Science, Applied Mathematics and Statistics, University of Girona, 17003 Girona, Spain)

  • Glòria Mateu-Figueras

    (Department of Computer Science, Applied Mathematics and Statistics, University of Girona, 17003 Girona, Spain)

  • Josep Antoni Martín-Fernández

    (Department of Computer Science, Applied Mathematics and Statistics, University of Girona, 17003 Girona, Spain)

Abstract

The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the L 1 -norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional L p -norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach.

Suggested Citation

  • Jordi Saperas-Riera & Glòria Mateu-Figueras & Josep Antoni Martín-Fernández, 2024. "L p -Norm for Compositional Data: Exploring the CoDa L 1 -Norm in Penalised Regression," Mathematics, MDPI, vol. 12(9), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1388-:d:1387489
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    References listed on IDEAS

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    1. G. S. Monti & P. Filzmoser, 2022. "Robust logistic zero-sum regression for microbiome compositional data," 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. 16(2), pages 301-324, June.
    2. Wei Lin & Pixu Shi & Rui Feng & Hongzhe Li, 2014. "Variable selection in regression with compositional covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 785-797.
    3. Jiarui Lu & Pixu Shi & Hongzhe Li, 2019. "Generalized linear models with linear constraints for microbiome compositional data," Biometrics, The International Biometric Society, vol. 75(1), pages 235-244, March.
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