IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v199y2024ics0047259x23000970.html
   My bibliography  Save this article

Asymptotic properties of hierarchical clustering in high-dimensional settings

Author

Listed:
  • Egashira, Kento
  • Yata, Kazuyoshi
  • Aoshima, Makoto

Abstract

In this study, three asymptotic behaviors of hierarchical clustering are defined and studied with strict conditions under several asymptotic settings, from large samples to high dimensionality, when having two independent populations. We proceed with the current comprehension of the asymptotic properties of hierarchical clustering in high-dimensional, low-sample-size (HDLSS) settings. For high-dimensional data, the asymptotic properties of hierarchical clustering are demonstrated under mild and practical settings, and we present simulation studies and hierarchical clustering performance discussions. Furthermore, hierarchical clustering was theoretically investigated when both the dimension and sample size approach infinity, and we generalized a latent number of populations considering hierarchical clustering in multiclass HDLSS settings.

Suggested Citation

  • Egashira, Kento & Yata, Kazuyoshi & Aoshima, Makoto, 2024. "Asymptotic properties of hierarchical clustering in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jmvana:v:199:y:2024:i:c:s0047259x23000970
    DOI: 10.1016/j.jmva.2023.105251
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000970
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105251?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. Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
    3. Borysov, Petro & Hannig, Jan & Marron, J.S., 2014. "Asymptotics of hierarchical clustering for growing dimension," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 465-479.
    4. Kazuyoshi Yata & Makoto Aoshima, 2020. "Geometric consistency of principal component scores for high‐dimensional mixture models and its application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 899-921, September.
    5. Liu, Yufeng & Hayes, David Neil & Nobel, Andrew & Marron, J. S, 2008. "Statistical Significance of Clustering for High-Dimension, Low–Sample Size Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1281-1293.
    6. Patrick K. Kimes & Yufeng Liu & David Neil Hayes & James Stephen Marron, 2017. "Statistical significance for hierarchical clustering," Biometrics, The International Biometric Society, vol. 73(3), pages 811-821, September.
    7. Charles M. Perou & Therese Sørlie & Michael B. Eisen & Matt van de Rijn & Stefanie S. Jeffrey & Christian A. Rees & Jonathan R. Pollack & Douglas T. Ross & Hilde Johnsen & Lars A. Akslen & Øystein Flu, 2000. "Molecular portraits of human breast tumours," Nature, Nature, vol. 406(6797), pages 747-752, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Richard Audoly & Rory McGee & Sergio Ocampo & Gonzalo Paz-Pardo, 2024. "The Life-Cycle Dynamics of Wealth Mobility," Staff Reports 1097, Federal Reserve Bank of New York.

    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. Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Marron, J.S., 2017. "Big Data in context and robustness against heterogeneity," Econometrics and Statistics, Elsevier, vol. 2(C), pages 73-80.
    3. Patrick K. Kimes & Yufeng Liu & David Neil Hayes & James Stephen Marron, 2017. "Statistical significance for hierarchical clustering," Biometrics, The International Biometric Society, vol. 73(3), pages 811-821, September.
    4. Kazuyoshi Yata & Makoto Aoshima, 2020. "Geometric consistency of principal component scores for high‐dimensional mixture models and its application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 899-921, September.
    5. Modarres, Reza, 2022. "A high dimensional dissimilarity measure," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    6. Yang, Xi & Hoadley, Katherine A. & Hannig, Jan & Marron, J.S., 2023. "Jackstraw inference for AJIVE data integration," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    7. Manish G & Anil Kumar Badana & Rama Rao Malla, 2017. "Emerging Diagnostic and Prognostic Biomarkers of Triple Negative Breast Cancer," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 1(3), pages 561-565, August.
    8. Jacob Elnaggar & Fern Tsien & Lucio Miele & Chindo Hicks & Clayton Yates & Melisa Davis, 2019. "An Integrative Genomics Approach for Associating Genetic Susceptibility with the Tumor Immune Microenvironment in Triple Negative Breast Cancer," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 15(1), pages 1-12, February.
    9. María Elena Martínez & Jonathan T Unkart & Li Tao & Candyce H Kroenke & Richard Schwab & Ian Komenaka & Scarlett Lin Gomez, 2017. "Prognostic significance of marital status in breast cancer survival: A population-based study," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-14, May.
    10. Yishai Shimoni, 2018. "Association between expression of random gene sets and survival is evident in multiple cancer types and may be explained by sub-classification," PLOS Computational Biology, Public Library of Science, vol. 14(2), pages 1-15, February.
    11. Marcin Pilarczyk & Mehdi Fazel-Najafabadi & Michal Kouril & Behrouz Shamsaei & Juozas Vasiliauskas & Wen Niu & Naim Mahi & Lixia Zhang & Nicholas A. Clark & Yan Ren & Shana White & Rashid Karim & Huan, 2022. "Connecting omics signatures and revealing biological mechanisms with iLINCS," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    12. Watanabe, Hiroki & Hyodo, Masashi & Seo, Takashi & Pavlenko, Tatjana, 2015. "Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 234-244.
    13. Richard Audoly & Rory McGee & Sergio Ocampo & Gonzalo Paz-Pardo, 2024. "The Life-Cycle Dynamics of Wealth Mobility," Staff Reports 1097, Federal Reserve Bank of New York.
    14. Junhee Seok & Ronald W Davis & Wenzhong Xiao, 2015. "A Hybrid Approach of Gene Sets and Single Genes for the Prediction of Survival Risks with Gene Expression Data," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-15, May.
    15. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.
    16. Qing Qu & Yan Mao & Xiao-chun Fei & Kun-wei Shen, 2013. "The Impact of Androgen Receptor Expression on Breast Cancer Survival: A Retrospective Study and Meta-Analysis," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-1, December.
    17. Sarah A Pendergrass & Everett Hayes & Giuseppina Farina & Raphael Lemaire & Harrison W Farber & Michael L Whitfield & Robert Lafyatis, 2010. "Limited Systemic Sclerosis Patients with Pulmonary Arterial Hypertension Show Biomarkers of Inflammation and Vascular Injury," PLOS ONE, Public Library of Science, vol. 5(8), pages 1-13, August.
    18. Yugo Nakayama & Kazuyoshi Yata & Makoto Aoshima, 2020. "Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1257-1286, October.
    19. Bourret, Pascale & Keating, Peter & Cambrosio, Alberto, 2011. "Regulating diagnosis in post-genomic medicine: Re-aligning clinical judgment?," Social Science & Medicine, Elsevier, vol. 73(6), pages 816-824, September.
    20. G. Gambardella & G. Viscido & B. Tumaini & A. Isacchi & R. Bosotti & D. di Bernardo, 2022. "A single-cell analysis of breast cancer cell lines to study tumour heterogeneity and drug response," Nature Communications, Nature, vol. 13(1), pages 1-12, December.

    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:199:y:2024:i:c:s0047259x23000970. 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.