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Clustering of longitudinal curves via a penalized method and EM algorithm

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  • Xin Wang

    (San Diego State University)

Abstract

In this article, a new method is proposed for clustering longitudinal curves. In the proposed method, clusters of mean functions are identified through a weighted concave pairwise fusion method. The EM algorithm and the alternating direction method of multipliers algorithm are combined to estimate the group structure, mean functions and principal components simultaneously. The proposed method also allows to incorporate the prior neighborhood information to have more meaningful groups by adding pairwise weights in the pairwise penalties. In the simulation study, the performance of the proposed method is compared to some existing clustering methods in terms of the accuracy for estimating the number of subgroups and mean functions. The results suggest that ignoring the covariance structure will have a great effect on the performance of estimating the number of groups and estimating accuracy. The effect of including pairwise weights is also explored in a spatial lattice setting to take into consideration of the spatial information. The results show that incorporating spatial weights will improve the performance. A real example is used to illustrate the proposed method.

Suggested Citation

  • Xin Wang, 2024. "Clustering of longitudinal curves via a penalized method and EM algorithm," Computational Statistics, Springer, vol. 39(3), pages 1485-1512, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01380-2
    DOI: 10.1007/s00180-023-01380-2
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    1. 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.
    2. 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.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Palma Daawin & Seonjin Kim & Tatjana Miljkovic, 2019. "Predictive Modeling of Obesity Prevalence for the U.S. Population," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(1), pages 64-81, January.
    5. Mingyang Ren & Sanguo Zhang & Qingzhao Zhang & Shuangge Ma, 2022. "Gaussian graphical model‐based heterogeneity analysis via penalized fusion," Biometrics, The International Biometric Society, vol. 78(2), pages 524-535, June.
    6. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    7. 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.
    8. Zhang, Xiaochen & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2022. "Subgroup analysis for high-dimensional functional regression," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    10. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    11. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    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. 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.
    14. Hui Huang & Yehua Li & Yongtao Guan, 2014. "Joint Modeling and Clustering Paired Generalized Longitudinal Trajectories With Application to Cocaine Abuse Treatment Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1412-1424, December.
    15. Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
    16. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    17. 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.
    18. Piaoxuan Xiao & Guochang Wang, 2022. "Partial functional linear regression with autoregressive errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(13), pages 4515-4536, June.
    19. 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.
    20. 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.
    21. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    22. Yehua Li & Naisyin Wang & Raymond J. Carroll, 2013. "Selecting the Number of Principal Components in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1284-1294, December.
    23. 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.
    24. Wang, Xin & Zhu, Zhengyuan & Zhang, Hao Helen, 2023. "Spatial heterogeneity automatic detection and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
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