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Biclustering analysis of functionals via penalized fusion

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  • Fang, Kuangnan
  • Chen, Yuanxing
  • Ma, Shuangge
  • Zhang, Qingzhao

Abstract

In biomedical data analysis, clustering is commonly conducted. Biclustering analysis conducts clustering in both the sample and covariate dimensions and can more comprehensively describe data heterogeneity. In most of the existing biclustering analyses, scalar measurements are considered. In this study, motivated by time-course gene expression data and other examples, we take the “natural next step” and consider the biclustering analysis of functionals under which, for each covariate of each sample, a function (to be exact, its values at discrete measurement points) is present. We develop a doubly penalized fusion approach, which includes a smoothness penalty for estimating functionals and, more importantly, a fusion penalty for clustering. Statistical properties are rigorously established, providing the proposed approach a strong ground. We also develop an effective ADMM algorithm and accompanying R code. Numerical analysis, including simulations, comparisons, and the analysis of two time-course gene expression data, demonstrates the practical effectiveness of the proposed approach.

Suggested Citation

  • Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001524
    DOI: 10.1016/j.jmva.2021.104874
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    References listed on IDEAS

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    1. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    2. Jeng‐Min Chiou & Pai‐Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699, September.
    3. 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.
    4. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    5. Chiou, Jeng-Min & Li, Pai-Ling, 2008. "Correlation-Based Functional Clustering via Subspace Projection," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1684-1692.
    6. Amandine Schmutz & Julien Jacques & Charles Bouveyron & Laurence Chèze & Pauline Martin, 2020. "Clustering multivariate functional data in group-specific functional subspaces," Computational Statistics, Springer, vol. 35(3), pages 1101-1131, September.
    7. 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.
    8. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    9. 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.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    11. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    12. Liu, Lili & Lin, Lu, 2019. "Subgroup analysis for heterogeneous additive partially linear models and its application to car sales data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 239-259.
    13. Shujie Ma & Jian Huang, 2017. "A Concave Pairwise Fusion Approach to Subgroup Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 410-423, January.
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