IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v15y2023i1d10.1007_s12561-022-09356-4.html
   My bibliography  Save this article

A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data

Author

Listed:
  • Binhuan Wang

    (New York University School of Medicine)

  • Lanqiu Yao

    (New York University School of Medicine)

  • Jiyuan Hu

    (New York University School of Medicine)

  • Huilin Li

    (New York University School of Medicine)

Abstract

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in a matrix-format data set, which can provide results in a checkerboard-like pattern for visualization and exploratory analysis in a wide array of domains. Multiple biclustering algorithms have been developed in the past two decades, among which the convex biclustering can guarantee a global optimum by formulating in as a convex optimization problem. On the other hand, the application of biclustering has not progressed in parallel with the algorithm techniques. For example, biclustering for increasingly popular microbiome research data is under-applied possibly due to its compositional constraints for each sample. In this manuscript, we propose a new convex biclustering algorithm, called the bi-ADMM, under general setups based on the ADMM algorithm, which is free of extra smoothing steps to visualize informative biclusters required by existing convex biclustering algorithms. Furthermore, we tailor it to the algorithm named biC-ADMM specifically to tackle compositional constraints confronted in microbiome data. The key step of our methods is to utilize the Sylvester Equation to derive the ADMM algorithm, which is new to the clustering research. The effectiveness of the proposed methods is examined through a variety of numerical experiments and a microbiome data application.

Suggested Citation

  • Binhuan Wang & Lanqiu Yao & Jiyuan Hu & Huilin Li, 2023. "A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 193-216, April.
  • Handle: RePEc:spr:stabio:v:15:y:2023:i:1:d:10.1007_s12561-022-09356-4
    DOI: 10.1007/s12561-022-09356-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-022-09356-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12561-022-09356-4?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. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Ian Holmes & Keith Harris & Christopher Quince, 2012. "Dirichlet Multinomial Mixtures: Generative Models for Microbial Metagenomics," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-15, February.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
    5. Li, Gen, 2020. "Generalized Co-clustering Analysis via Regularized Alternating Least Squares," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    6. Danny C. Sorensen & Yunkai Zhou, 2003. "Direct methods for matrix Sylvester and Lyapunov equations," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-27, January.
    7. Fang, Yixin & Wang, Junhui, 2012. "Selection of the number of clusters via the bootstrap method," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 468-477.
    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. Eric C. Chi & Genevera I. Allen & Richard G. Baraniuk, 2017. "Convex biclustering," Biometrics, The International Biometric Society, vol. 73(1), pages 10-19, March.
    2. Sakyajit Bhattacharya & Paul McNicholas, 2014. "A LASSO-penalized BIC for mixture model selection," 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. 8(1), pages 45-61, March.
    3. Peter Radchenko & Gourab Mukherjee, 2017. "Convex clustering via l 1 fusion penalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1527-1546, November.
    4. Sanjeena Subedi & Drew Neish & Stephen Bak & Zeny Feng, 2020. "Cluster analysis of microbiome data by using mixtures of Dirichlet–multinomial regression models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1163-1187, November.
    5. Zhao, Xin & Zhang, Jingru & Lin, Wei, 2023. "Clustering multivariate count data via Dirichlet-multinomial network fusion," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    6. Jie Chen & Joe Suzuki, 2021. "An Efficient Algorithm for Convex Biclustering," Mathematics, MDPI, vol. 9(23), pages 1-18, November.
    7. Pi, J. & Wang, Honggang & Pardalos, Panos M., 2021. "A dual reformulation and solution framework for regularized convex clustering problems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 844-856.
    8. Coraggio, Luca & Coretto, Pietro, 2023. "Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    9. Jiehuan Sun & Jose D. Herazo‐Maya & Philip L. Molyneaux & Toby M. Maher & Naftali Kaminski & Hongyu Zhao, 2019. "Regularized Latent Class Model for Joint Analysis of High‐Dimensional Longitudinal Biomarkers and a Time‐to‐Event Outcome," Biometrics, The International Biometric Society, vol. 75(1), pages 69-77, March.
    10. Tu, Wangshu & Browne, Ryan & Subedi, Sanjeena, 2024. "A mixture of logistic skew-normal multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    11. Minjie Wang & Tianyi Yao & Genevera I. Allen, 2023. "Supervised convex clustering," Biometrics, The International Biometric Society, vol. 79(4), pages 3846-3858, December.
    12. Vincent Audigier & Ndèye Niang, 2023. "Clustering with missing data: which equivalent for Rubin’s rules?," 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. 17(3), pages 623-657, September.
    13. Hong, Zhaoping & Lian, Heng, 2013. "Sparse-smooth regularized singular value decomposition," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 163-174.
    14. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    15. Miriam Aparicio, 2021. "Resiliency and Cooperation or Regarding Social and Collective Competencies for University Achievement. An Analysis from a Systemic Perspective," European Journal of Social Sciences Education and Research Articles, Revistia Research and Publishing, vol. 8, ejser_v8_.
    16. Yunpeng Zhao & Qing Pan & Chengan Du, 2019. "Logistic regression augmented community detection for network data with application in identifying autism‐related gene pathways," Biometrics, The International Biometric Society, vol. 75(1), pages 222-234, March.
    17. Wu, Han-Ming & Tien, Yin-Jing & Chen, Chun-houh, 2010. "GAP: A graphical environment for matrix visualization and cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 767-778, March.
    18. José E. Chacón, 2021. "Explicit Agreement Extremes for a 2 × 2 Table with Given Marginals," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 257-263, July.
    19. F. Marta L. Di Lascio & Andrea Menapace & Roberta Pappadà, 2024. "A spatially‐weighted AMH copula‐based dissimilarity measure for clustering variables: An application to urban thermal efficiency," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    20. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.

    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:spr:stabio:v:15:y:2023:i:1:d:10.1007_s12561-022-09356-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.