IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i9p1388-d1387489.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/9/1388/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/9/1388/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lingjing Jiang & Niina Haiminen & Anna‐Paola Carrieri & Shi Huang & Yoshiki Vázquez‐Baeza & Laxmi Parida & Ho‐Cheol Kim & Austin D. Swafford & Rob Knight & Loki Natarajan, 2022. "Utilizing stability criteria in choosing feature selection methods yields reproducible results in microbiome data," Biometrics, The International Biometric Society, vol. 78(3), pages 1155-1167, September.
    2. Yuan, Panxu & Jin, Changhan & Li, Gaorong, 2024. "FDR control for linear log-contrast models with high-dimensional compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    3. Sean M Devlin & Axel Martin & Irina Ostrovnaya, 2021. "Identifying prognostic pairwise relationships among bacterial species in microbiome studies," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-12, November.
    4. 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.
    5. Arun Srinivasan & Lingzhou Xue & Xiang Zhan, 2021. "Compositional knockoff filter for high‐dimensional regression analysis of microbiome data," Biometrics, The International Biometric Society, vol. 77(3), pages 984-995, September.
    6. 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.
    7. Jacob Fiksel & Scott Zeger & Abhirup Datta, 2022. "A transformation‐free linear regression for compositional outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(3), pages 974-987, September.
    8. Xu Lin & Hong-Mei Xiao & Hui-Min Liu & Wan-Qiang Lv & Jonathan Greenbaum & Rui Gong & Qiang Zhang & Yuan-Cheng Chen & Cheng Peng & Xue-Juan Xu & Dao-Yan Pan & Zhi Chen & Zhang-Fang Li & Rou Zhou & Xia, 2023. "Gut microbiota impacts bone via Bacteroides vulgatus-valeric acid-related pathways," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    9. Srinivasan, Arun & Xue, Lingzhou & Zhan, Xiang, 2023. "Identification of microbial features in multivariate regression under false discovery rate control," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    10. Zemin Zheng & Jinchi Lv & Wei Lin, 2021. "Nonsparse Learning with Latent Variables," Operations Research, INFORMS, vol. 69(1), pages 346-359, January.
    11. Huiwen Wang & Zhichao Wang & Shanshan Wang, 2021. "Sliced inverse regression method for multivariate compositional data modeling," Statistical Papers, Springer, vol. 62(1), pages 361-393, February.
    12. Rieser, Christopher & Filzmoser, Peter, 2023. "Extending compositional data analysis from a graph signal processing perspective," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    13. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    14. Licai Huang & Paul Little & Jeroen R. Huyghe & Qian Shi & Tabitha A. Harrison & Greg Yothers & Thomas J. George & Ulrike Peters & Andrew T. Chan & Polly A. Newcomb & Wei Sun, 2021. "A Statistical Method for Association Analysis of Cell Type Compositions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 373-385, December.
    15. Bingkai Wang & Brian S. Caffo & Xi Luo & Chin‐Fu Liu & Andreia V. Faria & Michael I. Miller & Yi Zhao & for the Alzheimer's Disease Neuroimaging Initiative*, 2022. "Regularized regression on compositional trees with application to MRI analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 541-561, June.
    16. Haixiang Zhang & Jun Chen & Zhigang Li & Lei Liu, 2021. "Testing for Mediation Effect with Application to Human Microbiome Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 313-328, July.
    17. Jeon, Jong-June & Kim, Yongdai & Won, Sungho & Choi, Hosik, 2020. "Primal path algorithm for compositional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    18. Cristofari, Andrea, 2023. "A decomposition method for lasso problems with zero-sum constraint," European Journal of Operational Research, Elsevier, vol. 306(1), pages 358-369.
    19. Liangliang Zhang & Yushu Shi & Robert R. Jenq & Kim‐Anh Do & Christine B. Peterson, 2021. "Bayesian compositional regression with structured priors for microbiome feature selection," Biometrics, The International Biometric Society, vol. 77(3), pages 824-838, September.
    20. Mishra, Aditya & Müller, Christian L., 2022. "Robust regression with compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1388-:d:1387489. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.