IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v38y2021i3d10.1007_s00357-021-09402-8.html
   My bibliography  Save this article

Co-clustering of Time-Dependent Data via the Shape Invariant Model

Author

Listed:
  • Alessandro Casa

    (University College Dublin)

  • Charles Bouveyron

    (Université Côte d’Azur)

  • Elena Erosheva

    (Université Côte d’Azur
    University of Washington)

  • Giovanna Menardi

    (University of Padova)

Abstract

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data, we need to account for relations among both time instants and variables and, at the same time, for subject heterogeneity. We propose a new co-clustering methodology for grouping individuals and variables simultaneously, designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the shape invariant model in the latent block model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that can be chosen on substantive grounds and provides parsimonious summaries of complex time-dependent data by partitioning data matrices into homogeneous blocks. Along with the explicit modelling of time evolution, these aspects allow for an easy interpretation of the clusters, from which also low-dimensional settings may benefit.

Suggested Citation

  • Alessandro Casa & Charles Bouveyron & Elena Erosheva & Giovanna Menardi, 2021. "Co-clustering of Time-Dependent Data via the Shape Invariant Model," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 626-649, October.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:3:d:10.1007_s00357-021-09402-8
    DOI: 10.1007/s00357-021-09402-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-021-09402-8
    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/s00357-021-09402-8?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. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," 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(3), pages 231-255, September.
    2. Donatello Telesca & Elena A. Erosheva & Derek A. Kreager & Ross L. Matsueda, 2012. "Modeling Criminal Careers as Departures From a Unimodal Population Age--Crime Curve: The Case of Marijuana Use," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1427-1440, December.
    3. Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    4. De la Cruz-Mesia, Rolando & Quintana, Fernando A. & Marshall, Guillermo, 2008. "Model-based clustering for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1441-1457, January.
    5. Valerie Robert & Yann Vasseur & Vincent Brault, 2021. "Comparing High-Dimensional Partitions with the Co-clustering Adjusted Rand Index," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 158-186, April.
    6. Selosse, Margot & Jacques, Julien & Biernacki, Christophe, 2020. "Model-based co-clustering for mixed type data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    7. Wyse, Jason & Friel, Nial & Latouche, Pierre, 2017. "Inferring structure in bipartite networks using the latent blockmodel and exact ICL," Network Science, Cambridge University Press, vol. 5(1), pages 45-69, March.
    8. van Dijk, A. & van Rosmalen, J.M. & Paap, R., 2009. "A Bayesian approach to two-mode clustering," Econometric Institute Research Papers EI 2009-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Telesca, Donatello & Inoue, Lurdes Y.T., 2008. "Bayesian Hierarchical Curve Registration," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 328-339, March.
    10. Govaert, Gérard & Nadif, Mohamed, 2008. "Block clustering with Bernoulli mixture models: Comparison of different approaches," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3233-3245, February.
    11. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    12. Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," 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. 5(4), pages 281-300, December.
    13. Charles Bouveyron & Laurent Bozzi & Julien Jacques & François‐Xavier Jollois, 2018. "The functional latent block model for the co‐clustering of electricity consumption curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 897-915, August.
    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. C. Biernacki & J. Jacques & C. Keribin, 2023. "A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 332-381, July.
    2. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Selosse, Margot & Jacques, Julien & Biernacki, Christophe, 2020. "Model-based co-clustering for mixed type data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Goffinet, Etienne & Lebbah, Mustapha & Azzag, Hanane & Loïc, Giraldi & Coutant, Anthony, 2022. "Functional non-parametric latent block model: A multivariate time series clustering approach for autonomous driving validation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    5. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    6. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," 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. 6(3), pages 219-247, October.
    8. Xin Yao & Yuanyuan Cheng & Li Zhou & Malin Song, 2022. "Green efficiency performance analysis of the logistics industry in China: based on a kind of machine learning methods," Annals of Operations Research, Springer, vol. 308(1), pages 727-752, January.
    9. Ja‐Yoon Jang & Hee‐Seok Oh & Yaeji Lim & Ying Kuen Cheung, 2021. "Ensemble clustering for step data via binning," Biometrics, The International Biometric Society, vol. 77(1), pages 293-304, March.
    10. M. P. B. Gallaugher & C. Biernacki & P. D. McNicholas, 2023. "Parameter-wise co-clustering for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1597-1619, September.
    11. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    12. Aghiles Salah & Mohamed Nadif, 2019. "Directional co-clustering," 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. 13(3), pages 591-620, September.
    13. Snježana Majstorović & Kristian Sabo & Johannes Jung & Matija Klarić, 2018. "Spectral methods for growth curve clustering," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 715-737, September.
    14. C. Denis & E. Lebarbier & C. Lévy‐Leduc & O. Martin & L. Sansonnet, 2020. "A novel regularized approach for functional data clustering: an application to milking kinetics in dairy goats," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 623-640, June.
    15. Gupta, Mayetri, 2014. "An evolutionary Monte Carlo algorithm for Bayesian block clustering of data matrices," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 375-391.
    16. Elvira Romano & Jorge Mateu & Ramon Giraldo, 2015. "On the performance of two clustering methods for spatial functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 467-492, October.
    17. Chabert-Liddell, Saint-Clair & Barbillon, Pierre & Donnet, Sophie & Lazega, Emmanuel, 2021. "A stochastic block model approach for the analysis of multilevel networks: An application to the sociology of organizations," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    18. Javier Albert-Smet & Aurora Torrente & Juan Romo, 2023. "Band depth based initialization of K-means for functional data clustering," 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(2), pages 463-484, June.
    19. Yifan Zhu & Chongzhi Di & Ying Qing Chen, 2019. "Clustering Functional Data with Application to Electronic Medication Adherence Monitoring in HIV Prevention Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 238-261, July.
    20. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.

    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:jclass:v:38:y:2021:i:3:d:10.1007_s00357-021-09402-8. 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.