Multivariate functional clustering and its application to typhoon data

We propose a multivariate nonlinear mixed effects model for clustering multiple longitudinal data. Advantages of the nonlinear mixed effects model are that it is easy to handle unbalanced data which highly occur in the longitudinal study, and it can take into account associations among longitudinal variables at a given time point. The joint modeling for multivariate longitudinal data, however, requires a high computational cost because numerous parameters are included in the model. To overcome this issue, we perform a pairwise fitting procedure based on a pseudo-likelihood function. Unknown parameters included in each bivariate model are estimated by the maximum likelihood method along with the EM algorithm, and then the number of basis functions included in the model is selected by model selection criteria. After estimating the model, a non-hierarchical clustering algorithm by self-organizing maps is applied to the predicted coefficient vectors of individual specific random effect functions. We present the results of the application of the proposed method to the analysis of data of typhoons that occurred between 2000 and 2017 in Asia.

[1]  Wolfgang Jank,et al.  Modelling price paths in on‐line auctions: smoothing sparse and unevenly sampled curves by using semiparametric mixed models , 2008 .

[2]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

[3]  Julien Jacques,et al.  Functional data clustering: a survey , 2013, Advances in Data Analysis and Classification.

[4]  Jeongyoun Ahn,et al.  Clustering multivariate functional data with phase variation , 2017, Biometrics.

[5]  Wensheng Guo.  Functional Mixed Effects Models , 2002 .

[6]  Julien Jacques,et al.  Model-based clustering for multivariate functional data , 2013, Comput. Stat. Data Anal..

[7]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[8]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[9]  Colin O. Wu,et al.  Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves , 2001, Biometrics.

[10]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[11]  Sadanori Konishi,et al.  Functional Cluster Analysis via Orthonormalized Gaussian Basis Expansions and Its Application , 2010, J. Classif..

[12]  Geert Verbeke,et al.  Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles , 2006, Biometrics.

[13]  H. Akaike.  A new look at the statistical model identification , 1974 .

[14]  M Giacofci,et al.  Wavelet‐Based Clustering for Mixed‐Effects Functional Models in High Dimension , 2011, Biometrics.

[15]  Catherine A. Sugar,et al.  Clustering for Sparsely Sampled Functional Data , 2003 .

[16]  John Hinde,et al.  Clustering longitudinal profiles using P-splines and mixed effects models applied to time-course gene expression data , 2014, Comput. Stat. Data Anal..

[17]  S. Konishi,et al.  Clustering for Functional Data via Nonlinear Mixed Effects Models , 2016 .

[18]  Hongzhe Li,et al.  Clustering of time-course gene expression data using a mixed-effects model with B-splines , 2003, Bioinform..

[19]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[20]  S. Müller,et al.  Sparse Pairwise Likelihood Estimation for Multivariate Longitudinal Mixed Models , 2018, Journal of the American Statistical Association.

[21]  Sadanori Konishi,et al.  NONLINEAR REGRESSION MODELING VIA REGULARIZED GAUSSIAN BASIS FUNCTIONS , 2007 .