Functional clustering and alignment methods with applications

We consider the issue of classification of functional data and, in particular, we deal with the problem of curve clustering when curves are misaligned. In the proposed setting, we aim at jointly aligning and clustering the curves, via the solution of an optimization problem. We describe an iterative procedure for the solution of the optimization problem, and we detail two alternative specifications of the procedure, a k-mean version and a k-medoid version. We illustrate via applications to real data the robustness of the alignment and clustering procedure under the different specifications.

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

[2]  J. Hartigan.  Asymptotic Distributions for Clustering Criteria , 1978 .

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

[4]  T. Gasser,et al.  Convergence and consistency results for self-modeling nonlinear regression , 1988 .

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

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

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

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

[9]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

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

[11]  Jeng-Min Chiou,et al.  Functional clustering and identifying substructures of longitudinal data , 2007 .

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

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

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

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

[16]  Hiroshi Yadohisa,et al.  Crisp and fuzzy k-means clustering algorithms for multivariate functional data , 2007, Comput. Stat..

[17]  David A. Steinman,et al.  An image-based modeling framework for patient-specific computational hemodynamics , 2008, Medical & Biological Engineering & Computing.

[18]  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 .

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

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

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

[22]  Simone Vantini,et al.  K-mean Alignment for Curve Clustering , 2010, Comput. Stat. Data Anal..

[23]  Hans-Georg Müller,et al.  Functional Data Analysis , 2016 .