CTW: Statistics of Time Warpings and Phase Variations

(November 13,2012 - November 16,2012 )

Organizers


J. S. Marron
Statistics and O. R., University of North Carolina, Chapel Hill
Jim Ramsay
Psychology, McGill University
Laura Sangalli
MOX - Dipartimento di Matematica, MOX - Dipartimento di Matematica, Politecnico di Milano
Anuj Srivastava
Statistics, Florida State University

Background: We often see in functional measurements of data over time, space and other continua that salient features in the resulting curves and surfaces vary in position from one recording to another. Children vary in the timing of puberty, human movement in activities like handwriting and golf swings speed and up and slow down from one instance to another , seasonal events like hurricanes arrive early some years and late in others, and traffic jams vary in location over city streets from one day to another. At the same time, each of the events can also vary in intensity. We refer to positional variation as phase variation, and intensity variation as amplitude variation; and it is now evident that many processes unfold over a system time that not only does not unroll at the same rate as physical clock time, but also tends to vary in a random way from one realization of a functional event to another. Amplitude and phase variation are illustrated in the Figure. Unfortunately most statistical technology, such as even the calculation of means, variances and correlations, cease to work properly if carried out over phase-varying data; that is, most of the classical statistical methodology was developed to assess only amplitude variation. For example, variation summary methods such as principal components analysis tend to spread the signal power of quite simple phase variation over a large number of components, and tend to blend amplitude and phase variation in confusing ways. As a consequence, methods for eliminating phase variation by nonlinearly transforming or warping time, space and so forth have been the subject of much recent research, and are referred to as registration methods. Registration leads to three interesting types of further analysis. First investigation of amplitude variation is straightforward, using conventional methods on the registered curves or surfaces. Second, various approaches to phase variation comes from study and analysis of the domain transformations, which are usually required to be diffeomorphic. Third, the joint variation, between the warpings and the amplitude variation can be understood and analyzed. This bi-partite or bi-stochastic nature of functional variation now appears to have very widespread implications for statistical science, and links directly to older problems such as shape analysis, as well as newer statistical topics such as dynamic systems. Fisher-Rao and Historical connection: One natural approach to such functional analysis is a Riemannian one, under the Fisher-Rao metric. While the parametric form of this metric has famously been used for analyzing (parametric) families, for example by Kass, Barndorff- Nielson, Le Cam, Amari, and others, its nonparametric version has proven important in curve and functional analysis (Srivastava, Younes, Mumford, etc). Historically, its use has been restricted to the submanifolds of parametric densities, deriving inference bounds and density comparisons. More recent work allows analysis of all densities, including nonparametric forms, and indeed to functions in general. Its invariance to parameterizations provides a natural framework for alignments of functions and curves, and for separating phase and amplitude variability in functional data. The workshop and subsequent meetings at SAMSI resulted in fruitful interactions between functional data analysts and shape analysts, and has led to this promising framework that it will be interesting to test in a variety of real applications. Workshop Ideas: Instead of the usual passive speaker-audience format, workshop activities will be centered around applying a wide variety of statistical methods to a common collection of data sets. The focus will be the various analytic approaches of several different Analysis Groups, to some common data sets, featuring careful discussion of the strengths and weaknesses of the various analyses. Main presentations will be made by the Analysis Groups, who will agree to analyze (before the workshop) each of the agreed upon data sets, and will present their results at the workshop. For context, each data set will have an Owner, who will be responsible for answering questions about the data while the analysis is under way, and who will at the beginning of the workshop give a brief description of the data, plus the main statistical questions. Following the analytic presentations, there will be group discussion with the goal of evaluation of the different methods used. It is anticipated that this will result in a list of the pros and cons of each approach, and in particular a clear view of the varying circumstances under which each method has advantages over the others. Dissemination of the results is intended to be through an article, co-authored by the major participants, aimed at a journal such as Statistical Science, or a top level computational statistics journal.

Tuesday, November 13, 2012
Time Session
10:30 AM
11:00 AM
Wei Wu - Time Warping of Neural Spike Train Data
Time Warping of Neural Spike Train Data
11:00 AM
11:30 AM
Inge Koch - Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
11:30 AM
12:00 PM
Jim Ramsay - The Registration of Juggling Data
The Registration of Juggling Data
12:00 PM
12:30 PM
Piercesare Secchi - The AneuRisk data
The AneuRisk data
02:00 PM
02:30 PM
Jim Ramsay - The Registration of Juggling Data
The Registration of Juggling Data
02:30 PM
03:30 PM
Alois Kneip - Some Conceptual problems of registration procedures
Some Conceptual problems of registration procedures
03:30 PM
04:15 PM
Anuj Srivastava - A Formal Definition of Phase and Amplitude in Functional Data
A Formal Definition of Phase and Amplitude in Functional Data
04:15 PM
04:45 PM
Ian McKeague - Detecting differentially expressed proteins: time warping and marginal screening
Detecting differentially expressed proteins: time warping and marginal screening
04:35 PM
05:00 PM
Ian Dryden - Bayesian Protein Analysis
Bayesian Protein Analysis
Wednesday, November 14, 2012
Time Session
09:00 AM
09:20 AM
Daniel Gervini - Maximum Likelihood Registration of ICA Curvature Trajectories
Maximum Likelihood Registration of ICA Curvature Trajectories
09:20 AM
09:40 AM
Laura Sangalli, Simone Vantini - Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
09:40 AM
10:00 AM
Ross Whitaker - Automatic Point Correspondence for Shape Analysis
Automatic Point Correspondence for Shape Analysis
11:00 AM
11:10 AM
John Aston - Joint Modelling of Phase and Amplitude Data
Joint Modelling of Phase and Amplitude Data
11:10 AM
11:20 AM
John Moriarty - Non-Gaussianity and Gaussian Process Regression
Non-Gaussianity and Gaussian Process Regression
11:20 AM
11:40 AM
Alessandro Veneziani - The Emergency Math Group at Emory University
The Emergency Math Group at Emory University
11:40 AM
12:20 PM
Victor Panaretos - On the Separation of Amplitude and Phase Variation in Finite Point Processes
On the Separation of Amplitude and Phase Variation in Finite Point Processes
02:30 PM
02:45 PM
Ian Dryden - Bayesian Protein Analysis
Bayesian Protein Analysis
03:00 PM
03:15 PM
Derek Tucker - Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework
Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework
03:45 PM
04:00 PM
Laura Sangalli - Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
04:15 PM
04:45 PM
Inge Koch - Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Thursday, November 15, 2012
Time Session
08:45 AM
08:55 AM
Simone Vantini - Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
08:55 AM
09:20 AM
David Hitchcock - Fitting and Registering the Spike Train Data
Fitting and Registering the Spike Train Data
09:20 AM
09:35 AM
Yoav Zemel - Point Process Variation
Point Process Variation
09:35 AM
09:50 AM
Xiaosun Lu - Spike Train
Spike Train
09:50 AM
10:05 AM
Pantelis Hadjipantelis - Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach
Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach
10:05 AM
10:25 AM
Wei Wu - Time Warping of Neural Spike Train Data
Time Warping of Neural Spike Train Data
11:00 AM
11:00 AM
Sebastian Kurtek - Analysis of Juggling Trajectories Using Square-Root Slope Functions
Analysis of Juggling Trajectories Using Square-Root Slope Functions
11:15 AM
11:30 AM
Juhyun Park - Joint analysis of phase and shape of curves: estimation of mean shape
Joint analysis of phase and shape of curves: estimation of mean shape
11:30 AM
11:45 AM
Simone Vantini - Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
11:45 AM
12:00 PM
Xiaosun Lu - Spike Train
Spike Train
01:30 PM
01:50 PM
Anders Tolver - Juggling dataset - identification of the right coordinate frame
Juggling dataset - identification of the right coordinate frame
01:45 PM
02:00 PM
Heiko Wagner - Enhanced Registration to Principal Components with Application to Juggling Data
Enhanced Registration to Principal Components with Application to Juggling Data
02:00 PM
02:20 PM
Jim Ramsay - The Registration of Juggling Data
The Registration of Juggling Data
03:15 PM
03:30 PM
Ana-Maria Staicu - AneuRisk Vascular Data
AneuRisk Vascular Data
03:30 PM
03:45 PM
Daniel Gervini - Maximum Likelihood Registration of ICA Curvature Trajectories
Maximum Likelihood Registration of ICA Curvature Trajectories
03:45 PM
04:00 PM
Qian Xie - Three-dimensional vascular geometry dataset
Three-dimensional vascular geometry dataset
04:00 PM
04:15 PM
Ian Dryden - Bayesian Protein Analysis
Bayesian Protein Analysis
04:30 PM
04:50 PM
Piercesare Secchi - The AneuRisk data
The AneuRisk data
04:50 PM
05:20 PM
Piercesare Secchi - The AneuRisk data
The AneuRisk data
Friday, November 16, 2012
Time Session
09:00 AM
09:30 AM
Ross Whitaker - Automatic Point Correspondence for Shape Analysis
Automatic Point Correspondence for Shape Analysis
09:30 AM
09:55 AM
Alessandro Veneziani - The Emergency Math Group at Emory University
The Emergency Math Group at Emory University
09:55 AM
10:30 AM
Sebastian Kurtek - Analysis of Juggling Trajectories Using Square-Root Slope Functions
Analysis of Juggling Trajectories Using Square-Root Slope Functions
11:30 AM
11:50 AM
Helle Sørensen - Complete chromatogram from a rape seed plant
Complete chromatogram from a rape seed plant
11:50 AM
12:10 PM
Kristen Irwin - Using Curve Registration to Improve Evolutionary Predictions in Function-Valued Traits
Using Curve Registration to Improve Evolutionary Predictions in Function-Valued Traits
12:10 PM
12:30 PM
Sara de Luna - Modelling varved lake sediment to detect past environment and climate changes
Modelling varved lake sediment to detect past environment and climate changes
02:00 PM
02:20 PM
John Aston - Joint Modelling of Phase and Amplitude Data
Joint Modelling of Phase and Amplitude Data
Name Affiliation
Ahn, Jeongyoun jyahn@uga.edu Statistics, University of Georgia
Arnqvist, Per per.arnqvist@math.umu.se Department of mathematics and mathematical statistics, Dept of math and mathematical statistics
Aston, John J.A.D.Aston@warwick.ac.uk Statistics, University of Warwick
Bernardi, Mara marasabina.bernardi@mail.polimi.it Mathematics, Politecnico di Milano
Cheng, Wen chengwen1985@gmail.com statistics, University of South Carolina
Dryden, Ian ian.dryden@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
Earls, Cecilia cae79@cornell.edu Statistics, Cornell University
Gervini, Daniel gervini@uwm.edu Mathematical Sciences, University of Wisconsin
Hadjipantelis, Pantelis p.z.hadjipantelis@warwick.ac.uk Statistics, Centre for Complexity Science, University of Warwick
Hitchcock, David hitchcock@stat.sc.edu Statistics, University of South Carolina
Irwin, Kristen k-irwin@wsu.edu School of Biological Sciences, Washington State University
Kneip, Alois akneip@uni-bonn.de Economics, University of Bonn
Koch, Inge inge.koch@adelaide.edu.au School of Mathematical Sciences, The University of Adelaide
Kurtek, Sebastian skurtek@stat.fsu.edu Statistics, The Ohio State University
Le, Huiling huiling.le@nottingham.ac.uk Scool of Mathematical Sciences, University of Nottingham
Liu, Xueli xuliu@coh.org Biostatistics, City of Hope
Lu, Xiaosun xiaosun@live.unc.edu STOR, University of North Carolina, Chapel Hill
Marron, J. S. marron@email.unc.edu Statistics and O. R., University of North Carolina, Chapel Hill
McKeague, Ian im2131@columbia.edu Biostatistics, Columbia University
Moriarty, John John.Moriarty@manchester.ac.uk School of Mathematics, University of Manchester
Muller, Martha mmul@life.ku.dk Mathematics, University of Copenhagen
Panaretos, Victor victor.panaretos@epfl.ch Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL)
Park, Juhyun juhyun.park@lancaster.ac.uk Mathematics and Statistics, Lancaster University
Patriarca, Mirco mirco.patriarca@mail.polimi.it Mathematics, Politecnico di Milano
Po?, Dominik dposs@uni-bonn.de BGSE, Uni Bonn
Ramsay, Jim ramsay@psych.mcgill.ca Psychology, McGill University
Sangalli, Laura laura.sangalli@polimi.it MOX - Dipartimento di Matematica, MOX - Dipartimento di Matematica, Politecnico di Milano
Secchi, Piercesare piercesare.secchi@polimi.it Mathematics, Politecnico di Milano
Seyed Nourollah, Mousavi nourollah@math.ku.dk Mathematical of Sciences, University of Copenhagen
S�rensen, Helle helle@math.ku.dk Dept. of Mathematical Sciences, University of Copenhagen
Sjostedt de Luna, Sara sara.de.luna@math.umu.se Dept Mathematics and Mathematical Statistics, Umeå University
Srivastava, Anuj asrivastava@fsu.edu Statistics, Florida State University
Staicu, Ana-Maria ana-maria_staicu@ncsu.edu Statistics, North Carolina State University
Tolver, Anders tolver@life.ku.dk Department of Mathematical Sciences, University of Copenhagen
Trouve, Alain trouve@cmla.ens-cachan.fr Mathematics, 'Ecole Normale Sup'erieure de Cachan
Tucker, James dtucker@stat.fsu.edu Statistics, Florida State University
Vantini, Simone simone.vantini@polimi.it MOX - Dipartimento di Matematica, Politecnico di Milano
Veneziani, Alessandro ale@mathcs.emory.edu Mathematics and Computer Science, Emory University
Wagner, Heiko iefak2000@gmail.com Institut für Statistik, Uni Bonn
Whitaker, Ross whitaker@cs.utah.edu School of Computing, University of Utah
Wu, Wei wwu@stat.fsu.edu Department of Statistics, Florida State University
Xie, Qian qxie@stat.fsu.edu Statistics, Florida State University
Zemel, Yoav zamsh7@gmail.com Mathematics, École Polytechnique Fédérale de Lausanne
Joint Modelling of Phase and Amplitude Data
Joint Modelling of Phase and Amplitude Data
Talking to Beetles about Warping
Talking to Beetles about Warping
Bayesian Protein Analysis
Bayesian Protein Analysis
Registration Invariance
Registration Invariance
Carotid artery shape analysis
Carotid artery shape analysis
Maximum Likelihood Registration of ICA Curvature Trajectories
Maximum Likelihood Registration of ICA Curvature Trajectories
Maximum Likelihood Registration of ICA Curvature Trajectories
Maximum Likelihood Registration of ICA Curvature Trajectories
Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach
Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach
Fitting and Registering the Spike Train Data
Fitting and Registering the Spike Train Data
Using Curve Registration to Improve Evolutionary Predictions in Function-Valued Traits
Using Curve Registration to Improve Evolutionary Predictions in Function-Valued Traits
Some Conceptual problems of registration procedures
Some Conceptual problems of registration procedures
Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Fisher Rao Alignment of Proteomic Data
Fisher Rao Alignment of Proteomic Data
Analysis of Juggling Trajectories Using Square-Root Slope Functions
Analysis of Juggling Trajectories Using Square-Root Slope Functions
Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields
Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields
Spike Train
Spike Train
Analysis of Juggling Data
Analysis of Juggling Data
Detecting differentially expressed proteins: time warping and marginal screening
Detecting differentially expressed proteins: time warping and marginal screening
Non-Gaussianity and Gaussian Process Regression
Non-Gaussianity and Gaussian Process Regression
On the Separation of Amplitude and Phase Variation in Finite Point Processes
On the Separation of Amplitude and Phase Variation in Finite Point Processes
Joint analysis of phase and shape of curves: estimation of mean shape
Joint analysis of phase and shape of curves: estimation of mean shape
The Registration of Juggling Data
The Registration of Juggling Data
Multivariate and Functional Principal Components without Eigenanalysis
Multivariate and Functional Principal Components without Eigenanalysis
Analysis of Juggling Trajectories using Square-Root Slope Functions
Analysis of Juggling Trajectories using Square-Root Slope Functions
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
The AneuRisk data
The AneuRisk data
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Thursday Afternoon Discussion
Thursday Afternoon Discussion led by Piercesare Secchi
Complete chromatogram from a rape seed plant
Complete chromatogram from a rape seed plant
Modelling varved lake sediment to detect past environment and climate changes
Modelling varved lake sediment to detect past environment and climate changes
A Formal Definition of Phase and Amplitude in Functional Data
A Formal Definition of Phase and Amplitude in Functional Data
AneuRisk Vascular Data
AneuRisk Vascular Data
Juggling dataset - identification of the right coordinate frame
Juggling dataset - identification of the right coordinate frame
Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework
Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework
Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
Joint Clustering and Alignment of functional Data: The K-mean Alignment Algoithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
The Emergency Math Group at Emory University
The Emergency Math Group at Emory University
Image Registration: Tracking the motion of vascular geometries (and more)
Image Registration: Tracking the motion of vascular geometries (and more)
Enhanced Registration to Principal Components with Application to Juggling Data
Enhanced Registration to Principal Components with Application to Juggling Data
Automatic Point Correspondence for Shape Analysis
Automatic Point Correspondence for Shape Analysis
Ensemble-Based Registration of Functions and Surfaces
Ensemble-Based Registration of Functions and Surfaces
Time Warping of Neural Spike Train Data
Time Warping of Neural Spike Train Data
Registration of Neural Spike Train Data
Registration of Neural Spike Train Data
Three-dimensional vascular geometry dataset
Three-dimensional vascular geometry dataset
Point Process Variation
Point Process Variation
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Joint Modelling of Phase and Amplitude Data
John Aston Joint Modelling of Phase and Amplitude Data

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Multivariate and Functional Principal Components without Eigenanalysis
Jim Ramsay Multivariate and Functional Principal Components without Eigenanalysis

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Analysis of Juggling Trajectories using Square-Root Slope Functions
Jim Ramsay Analysis of Juggling Trajectories using Square-Root Slope Functions

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The Registration of Juggling Data
Jim Ramsay The Registration of Juggling Data

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Three-dimensional vascular geometry dataset
Qian Xie Three-dimensional vascular geometry dataset

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Registration of Neural Spike Train Data
Wei Wu Registration of Neural Spike Train Data

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Time Warping of Neural Spike Train Data
Wei Wu Time Warping of Neural Spike Train Data

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Enhanced Registration to Principal Components with Application to Juggling Data
Heiko Wagner Enhanced Registration to Principal Components with Application to Juggling Data

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Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework
James Tucker Alignment and Analysis of Proteomics Data using Square Root Slope Function Framework

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Juggling dataset - identification of the right coordinate frame
Anders Tolver Juggling dataset - identification of the right coordinate frame

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A Formal Definition of Phase and Amplitude in Functional Data
Anuj Srivastava A Formal Definition of Phase and Amplitude in Functional Data

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Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Laura Sangalli Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm

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Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm
Laura Sangalli, Simone Vantini Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm

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Joint analysis of phase and shape of curves: estimation of mean shape
Juhyun Park Joint analysis of phase and shape of curves: estimation of mean shape

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Non-Gaussianity and Gaussian Process Regression
John Moriarty Non-Gaussianity and Gaussian Process Regression

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Detecting differentially expressed proteins: time warping and marginal screening
Ian McKeague Detecting differentially expressed proteins: time warping and marginal screening

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Analysis of Juggling Data
Xiaosun Lu Analysis of Juggling Data

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Spike Train
Xiaosun Lu Spike Train

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Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields
Sebastian Kurtek Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields

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Analysis of Juggling Trajectories Using Square-Root Slope Functions
Sebastian Kurtek Analysis of Juggling Trajectories Using Square-Root Slope Functions

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Fisher Rao Alignment of Proteomic Data
Inge Koch Fisher Rao Alignment of Proteomic Data

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Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry
Inge Koch Acute Myeloid Leukaemia Data from Label-Free Liquid Chromatography Mass Spectrometry

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Some Conceptual problems of registration procedures
Alois Kneip Some Conceptual problems of registration procedures

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Fitting and Registering the Spike Train Data
David Hitchcock Fitting and Registering the Spike Train Data

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Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach
Pantelis Hadjipantelis Unifying Amplitude and Phase Analysis: A functional Multivariate Mixed-effects Approach

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Maximum Likelihood Registration of ICA Curvature Trajectories
Daniel Gervini Maximum Likelihood Registration of ICA Curvature Trajectories

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Maximum Likelihood Registration of ICA Curvature Trajectories
Daniel Gervini Maximum Likelihood Registration of ICA Curvature Trajectories

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Carotid artery shape analysis
Ian Dryden Carotid artery shape analysis

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Registration Invariance
Ian Dryden Registration Invariance

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Bayesian Protein Analysis
Ian Dryden Bayesian Protein Analysis