IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v110y2015i511p946-961.html
   My bibliography  Save this article

Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data

Author

Listed:
  • Chao Huang
  • Martin Styner
  • Hongtu Zhu

Abstract

An important goal in image analysis is to cluster and recognize objects of interest according to the shapes of their boundaries. Clustering such objects faces at least four major challenges including a curved shape space, a high-dimensional feature space, a complex spatial correlation structure, and shape variation associated with some covariates (e.g., age or gender). The aim of this article is to develop a penalized model-based clustering framework to cluster landmark-based planar shape data, while explicitly addressing these challenges. Specifically, a mixture of offset-normal shape factor analyzers (MOSFA) is proposed with mixing proportions defined through a regression model (e.g., logistic) and an offset-normal shape distribution in each component for data in the curved shape space. A latent factor analysis model is introduced to explicitly model the complex spatial correlation. A penalized likelihood approach with both adaptive pairwise fused Lasso penalty function and L 2 penalty function is used to automatically realize variable selection via thresholding and deliver a sparse solution. Our real data analysis has confirmed the excellent finite-sample performance of MOSFA in revealing meaningful clusters in the corpus callosum shape data obtained from the Attention Deficit Hyperactivity Disorder-200 (ADHD-200) study. Supplementary materials for this article are available online.

Suggested Citation

  • Chao Huang & Martin Styner & Hongtu Zhu, 2015. "Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 946-961, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:946-961
    DOI: 10.1080/01621459.2015.1034802
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2015.1034802
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2015.1034802?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. Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
    2. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
    3. Xiaoyan Shi & Hongtu Zhu & Joseph G. Ibrahim & Faming Liang & Jeffrey Lieberman & Martin Styner, 2012. "Intrinsic Regression Models for Medial Representation of Subcortical Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 12-23, March.
    4. Amaral, G.J.A. & Dryden, I.L. & Wood, Andrew T.A., 2007. "Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 695-707, June.
    5. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    6. Walter Ledermann, 1937. "On the rank of the reduced correlational matrix in multiple-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 2(2), pages 85-93, June.
    7. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
    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. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.
    2. Ruite Guo & Hwiyoung Lee & Vic Patrangenaru, 2023. "Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1178-1204, August.
    3. Lizhen Lin & Brian St. Thomas & Hongtu Zhu & David B. Dunson, 2017. "Extrinsic Local Regression on Manifold-Valued Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1261-1273, July.

    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. Galimberti, Giuliano & Montanari, Angela & Viroli, Cinzia, 2009. "Penalized factor mixture analysis for variable selection in clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4301-4310, October.
    2. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.
    3. Papastamoulis, Panagiotis, 2018. "Overfitting Bayesian mixtures of factor analyzers with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 220-234.
    4. 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.
    5. McNicholas, P.D. & Murphy, T.B. & McDaid, A.F. & Frost, D., 2010. "Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 711-723, March.
    6. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    7. Sharon X. Lee & Tsung-I Lin & Geoffrey J. McLachlan, 2021. "Mixtures of factor analyzers with scale mixtures of fundamental skew normal distributions," 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. 15(2), pages 481-512, June.
    8. Wan-Lun Wang & Tsung-I Lin, 2020. "Automated learning of mixtures of factor analysis models with missing information," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1098-1124, December.
    9. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2022. "Gaussian mixture model with an extended ultrametric covariance structure," 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(2), pages 399-427, June.
    10. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
    11. Alex Sharp & Glen Chalatov & Ryan P. Browne, 2023. "A dual subspace parsimonious mixture of matrix normal distributions," 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 801-822, September.
    12. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    13. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    14. Wang, Wan-Lun, 2015. "Mixtures of common t-factor analyzers for modeling high-dimensional data with missing values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 223-235.
    15. Coffey, N. & Hinde, J. & Holian, E., 2014. "Clustering longitudinal profiles using P-splines and mixed effects models applied to time-course gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 14-29.
    16. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic factor analyzers," 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. 10(4), pages 423-440, December.
    17. Wang, Wan-Lun, 2013. "Mixtures of common factor analyzers for high-dimensional data with missing information," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 120-133.
    18. Wan-Lun Wang & Tsung-I Lin, 2023. "Model-based clustering via mixtures of unrestricted skew normal factor analyzers with complete and incomplete data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 787-817, September.
    19. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," 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 745-775, September.
    20. Xiang Lu & Yaoxiang Li & Tanzy Love, 2021. "On Bayesian Analysis of Parsimonious Gaussian Mixture Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 576-593, October.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:110:y:2015:i:511:p:946-961. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.