IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v160y2021ics0167947321000530.html
   My bibliography  Save this article

FunCC: A new bi-clustering algorithm for functional data with misalignment

Author

Listed:
  • Galvani, Marta
  • Torti, Agostino
  • Menafoglio, Alessandra
  • Vantini, Simone

Abstract

The problem of bi-clustering functional data, which has recently been addressed in literature, is considered. A definition of ideal functional bi-cluster is given and a novel bi-clustering method, called Functional Cheng and Church (FunCC), is developed. The introduced algorithm searches for non-overlapping and non-exhaustive bi-clusters in a set of functions which are naturally ordered in matrix structure through a non-parametric deterministic iterative procedure. Moreover, the possible misalignment of the data, which is a common problem when dealing with functions, is taken into account. Hence, the FunCC algorithm is extended obtaining a model able to jointly bi-cluster and align curves. Different simulation studies are performed to show the potential of the introduced method and to compare it with state-of-the-art methods. The model is also applied on a real case study allowing to discover the spatio-temporal patterns of a bike-sharing system.

Suggested Citation

  • Galvani, Marta & Torti, Agostino & Menafoglio, Alessandra & Vantini, Simone, 2021. "FunCC: A new bi-clustering algorithm for functional data with misalignment," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
  • Handle: RePEc:eee:csdana:v:160:y:2021:i:c:s0167947321000530
    DOI: 10.1016/j.csda.2021.107219
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321000530
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2021.107219?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. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Veneziani, Alessandro, 2009. "A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 37-48.
    2. Simone Vantini, 2012. "On the definition of phase and amplitude variability in functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 676-696, December.
    3. 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.
    4. Kaziska, David & Srivastava, Anuj, 2007. "Gait-Based Human Recognition by Classification of Cyclostationary Processes on Nonlinear Shape Manifolds," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1114-1124, December.
    5. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
    6. 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. 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.
    2. Piercesare Secchi & Simone Vantini & Valeria Vitelli, 2015. "Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 279-300, July.
    3. Simone Vantini, 2012. "On the definition of phase and amplitude variability in functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 676-696, December.
    4. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Dimeglio, Chloé & Gallón, Santiago & Loubes, Jean-Michel & Maza, Elie, 2014. "A robust algorithm for template curve estimation based on manifold embedding," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 373-386.
    6. 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.
    7. Menafoglio, Alessandra & Petris, Giovanni, 2016. "Kriging for Hilbert-space valued random fields: The operatorial point of view," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 84-94.
    8. 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.
    9. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
    10. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    11. Pedro C. Álvarez-Esteban & Luis A. García-Escudero, 2022. "Robust clustering of functional directional 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(1), pages 181-199, March.
    12. Gianluca Sottile & Giada Adelfio, 2019. "Clusters of effects curves in quantile regression models," Computational Statistics, Springer, vol. 34(2), pages 551-569, June.
    13. Francesca Ieva & Anna Paganoni, 2015. "Discussion of “multivariate functional outlier detection” by M. Hubert, P. Rousseeuw and P. Segaert," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 217-221, July.
    14. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    15. Niels Lundtorp Olsen & Bo Markussen & Lars Lau Raket, 2018. "Simultaneous inference for misaligned multivariate functional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1147-1176, November.
    16. Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.
    17. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    18. Selosse, Margot & Jacques, Julien & Biernacki, Christophe, 2020. "Model-based co-clustering for mixed type data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Slaets, Leen & Claeskens, Gerda & Silverman, Bernard W., 2013. "Warping Functional Data in R and C via a Bayesian Multiresolution Approach," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i03).
    20. Antonio Elías & Raúl Jiménez & Han Lin Shang, 2023. "Depth-based reconstruction method for incomplete functional data," Computational Statistics, Springer, vol. 38(3), pages 1507-1535, September.

    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:csdana:v:160:y:2021:i:c:s0167947321000530. 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/locate/csda .

    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.