IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v198y2023ics0047259x23000556.html
   My bibliography  Save this article

Extending compositional data analysis from a graph signal processing perspective

Author

Listed:
  • Rieser, Christopher
  • Filzmoser, Peter

Abstract

Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is known that a relationship only exists between very specific variables (e.g. for metabolomic pathways), while for other pairs a relationship does not exist. Modeling absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. This paper links compositional data analysis with graph signal processing, and it extends the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance and compositional coherence. A real data example from bioinformatics underlines the usefulness of this approach.

Suggested Citation

  • Rieser, Christopher & Filzmoser, Peter, 2023. "Extending compositional data analysis from a graph signal processing perspective," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x23000556
    DOI: 10.1016/j.jmva.2023.105209
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000556
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105209?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    3. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    4. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    5. Zachary D Kurtz & Christian L Müller & Emily R Miraldi & Dan R Littman & Martin J Blaser & Richard A Bonneau, 2015. "Sparse and Compositionally Robust Inference of Microbial Ecological Networks," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-25, May.
    6. Karel Hron & Lubomír Kubáček, 2011. "Statistical properties of the total variation estimator for compositional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 221-230, September.
    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. Juan José Egozcue & Vera Pawlowsky-Glahn, 2019. "Compositional data: the sample space and its structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-638, September.
    2. Duo Jiang & Thomas Sharpton & Yuan Jiang, 2021. "Microbial Interaction Network Estimation via Bias-Corrected Graphical Lasso," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 329-350, July.
    3. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    4. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    5. Murat Genç, 2022. "A new double-regularized regression using Liu and lasso regularization," Computational Statistics, Springer, vol. 37(1), pages 159-227, March.
    6. Siwei Xia & Yuehan Yang & Hu Yang, 2022. "Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 255-277, March.
    7. 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.
    8. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Mishra, Aditya & Müller, Christian L., 2022. "Robust regression with compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    10. 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.
    11. Ines Wilms & Jacob Bien, 2021. "Tree-based Node Aggregation in Sparse Graphical Models," Papers 2101.12503, arXiv.org.
    12. Zachary D Kurtz & Christian L Müller & Emily R Miraldi & Dan R Littman & Martin J Blaser & Richard A Bonneau, 2015. "Sparse and Compositionally Robust Inference of Microbial Ecological Networks," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-25, May.
    13. Liu, Weidong & Luo, Xi, 2015. "Fast and adaptive sparse precision matrix estimation in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 153-162.
    14. Patrick L. Combettes & Christian L. Müller, 2021. "Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 217-242, July.
    15. Laura Freijeiro‐González & Manuel Febrero‐Bande & Wenceslao González‐Manteiga, 2022. "A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates," International Statistical Review, International Statistical Institute, vol. 90(1), pages 118-145, April.
    16. Chieh Lo & Radu Marculescu, 2017. "MPLasso: Inferring microbial association networks using prior microbial knowledge," PLOS Computational Biology, Public Library of Science, vol. 13(12), pages 1-20, December.
    17. 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.
    18. 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.
    19. Xiao Guo & Hai Zhang, 2020. "Sparse directed acyclic graphs incorporating the covariates," Statistical Papers, Springer, vol. 61(5), pages 2119-2148, October.
    20. Yang, Yuehan & Xia, Siwei & Yang, Hu, 2023. "Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures," Computational Statistics & Data Analysis, Elsevier, vol. 178(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:eee:jmvana:v:198:y:2023:i:c:s0047259x23000556. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.