K-mean Alignment for Curve Clustering

The problem of curve clustering when curves are misaligned is considered. A novel algorithm is described, which jointly clusters and aligns curves. The proposed procedure efficiently decouples amplitude and phase variability; in particular, it is able to detect amplitude clusters while simultaneously disclosing clustering structures in the phase, pointing out features that can neither be captured by simple curve clustering nor by simple curve alignment. The procedure is illustrated via simulation studies and applications to real data.

[1]  Ruben H. Zamar,et al.  Comparing the shapes of regression functions , 2000 .

[2]  Masahiro Mizuta,et al.  Functional Clustering and Functional Principal Points , 2007, KES.

[3]  A. Veneziani,et al.  A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery , 2009 .

[4]  Jeng-Min Chiou,et al.  Identifying cluster number for subspace projected functional data clustering , 2011, Comput. Stat. Data Anal..

[5]  James O. Ramsay,et al.  Functional Data Analysis , 2005 .

[6]  William G. Cochran,et al.  Contributions to statistics , 1983 .

[7]  Xueli Liu,et al.  Simultaneous curve registration and clustering for functional data , 2009, Comput. Stat. Data Anal..

[8]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[9]  Simone Vantini,et al.  Efficient estimation of three‐dimensional curves and their derivatives by free‐knot regression splines, applied to the analysis of inner carotid artery centrelines , 2009 .

[10]  R. Largo,et al.  An analysis of variance of the pubertal and midgrowth spurts for length and width. , 1999, Annals of human biology.

[11]  Olivier Meste,et al.  Core Shape modelling of a set of curves , 2010, Comput. Stat. Data Anal..

[12]  N. Altman,et al.  Self‐modelling regression for longitudinal data with time‐invariant covariates , 2004 .

[13]  E. A. Sylvestre,et al.  Self Modeling Nonlinear Regression , 1972 .

[14]  Mia Hubert,et al.  Phase and Amplitude-Based Clustering for Functional Data , 2012, Comput. Stat. Data Anal..

[15]  S. Vantini.  On the definition of phase and amplitude variability in functional data analysis , 2009, TEST.

[16]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[17]  Frédéric Ferraty,et al.  Functional Nonparametric Statistics in Action , 2006 .

[18]  H. Müller,et al.  Time-synchronized clustering of gene expression trajectories. , 2008, Biostatistics.

[19]  Gareth M. James.  Curve alignment by moments , 2007, 0712.1425.

[20]  Juan Antonio Cuesta-Albertos,et al.  Impartial trimmed k-means for functional data , 2007, Comput. Stat. Data Anal..

[21]  J. Ramsay,et al.  Curve registration , 2018, Oxford Handbooks Online.

[22]  T. Gasser,et al.  Self‐modelling warping functions , 2004 .

[23]  Anuj Srivastava,et al.  Gait-Based Human Recognition by Classification of Cyclostationary Processes on Nonlinear Shape Manifolds , 2007 .

[24]  Lurdes Y. T. Inoue,et al.  Bayesian Hierarchical Curve Registration , 2008 .

[25]  Yuedong Wang,et al.  Semiparametric Nonlinear Mixed-Effects Models and Their Applications , 2001 .

[26]  Thaddeus Tarpey,et al.  Clustering Functional Data , 2003, J. Classif..

[27]  F. Earnest,et al.  Krayenbühl/Yasargil Cerebral Angiography , 1983 .

[28]  T. Gasser,et al.  Contribution of growth phases to adult size. , 2000, Annals of human biology.

[29]  D. Bates,et al.  Nonlinear mixed effects models for repeated measures data. , 1990, Biometrics.

[30]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .