### Organizers

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 | |
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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 - Multivariate and Functional Principal Components without Eigenanalysis Multivariate and Functional Principal Components without Eigenanalysis |

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 - Registration Invariance Registration Invariance |

Wednesday, November 14, 2012 | |
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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 - Fisher Rao Alignment of Proteomic Data Fisher Rao Alignment of Proteomic Data |

Thursday, November 15, 2012 | |
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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 - Registration of Neural Spike Train Data Registration 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 Algorithm Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm |

11:45 AM 12:00 PM | Xiaosun Lu - Analysis of Juggling Data Analysis of Juggling Data |

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 - Analysis of Juggling Trajectories using Square-Root Slope Functions Analysis of Juggling Trajectories using Square-Root Slope Functions |

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 - Carotid artery shape analysis Carotid artery shape analysis |

04:30 PM 04:50 PM | Piercesare Secchi - Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm Joint Clustering and Alignment of Functional Data: The K-mean Alignment Algorithm |

04:50 PM 05:20 PM | Piercesare Secchi - Thursday Afternoon Discussion Thursday Afternoon Discussion led by Piercesare Secchi |

Friday, November 16, 2012 | |
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Time | Session |

09:00 AM 09:30 AM | Ross Whitaker - Ensemble-Based Registration of Functions and Surfaces Ensemble-Based Registration of Functions and Surfaces |

09:30 AM 09:55 AM | Alessandro Veneziani - Image Registration: Tracking the motion of vascular geometries (and more) Image Registration: Tracking the motion of vascular geometries (and more) |

09:55 AM 10:30 AM | Sebastian Kurtek - Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields Registration of Surfaces using Square-Root Functions and Square-Root Normal Fields |

11:30 AM 11:50 AM | Helle SÃ¸rensen - 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 - Talking to Beetles about Warping Talking to Beetles about Warping |

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 FÃƒÂ©dÃƒÂ©rale 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 |

PoÃ?, 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 |

Sï¿½rensen, 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, UmeÃƒÂ¥ 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 fÃƒÂ¼r 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, Ãƒâ€°cole Polytechnique FÃƒÂ©dÃƒÂ©rale de Lausanne |

**Joint Modelling of Phase and Amplitude Data**

John Aston Joint Modelling of Phase and Amplitude Data

**Multivariate and Functional Principal Components without Eigenanalysis**

Jim Ramsay Multivariate and Functional Principal Components without Eigenanalysis

**Analysis of Juggling Trajectories using Square-Root Slope Functions**

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

**The Registration of Juggling Data**

Jim Ramsay The Registration of Juggling Data

**Three-dimensional vascular geometry dataset**

Qian Xie Three-dimensional vascular geometry dataset

**Registration of Neural Spike Train Data**

Wei Wu Registration of Neural Spike Train Data

**Time Warping of Neural Spike Train Data**

Wei Wu Time Warping of Neural Spike Train Data

**Enhanced Registration to Principal Components with Application to Juggling Data**

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

**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

**Juggling dataset - identification of the right coordinate frame**

Anders Tolver Juggling dataset - identification of the right coordinate frame

**A Formal Definition of Phase and Amplitude in Functional Data**

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

**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

**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

**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

**Non-Gaussianity and Gaussian Process Regression**

John Moriarty Non-Gaussianity and Gaussian Process Regression

**Detecting differentially expressed proteins: time warping and marginal screening**

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

**Analysis of Juggling Data**

Xiaosun Lu Analysis of Juggling Data

**Spike Train**

Xiaosun Lu Spike Train

**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

**Analysis of Juggling Trajectories Using Square-Root Slope Functions**

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

**Fisher Rao Alignment of Proteomic Data**

Inge Koch Fisher Rao Alignment of Proteomic Data

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

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

**Some Conceptual problems of registration procedures**

Alois Kneip Some Conceptual problems of registration procedures

**Fitting and Registering the Spike Train Data**

David Hitchcock Fitting and Registering the Spike Train Data

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

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

**Maximum Likelihood Registration of ICA Curvature Trajectories**

Daniel Gervini Maximum Likelihood Registration of ICA Curvature Trajectories

**Maximum Likelihood Registration of ICA Curvature Trajectories**

Daniel Gervini Maximum Likelihood Registration of ICA Curvature Trajectories

**Carotid artery shape analysis**

Ian Dryden Carotid artery shape analysis

**Registration Invariance**

Ian Dryden Registration Invariance

**Bayesian Protein Analysis**

Ian Dryden Bayesian Protein Analysis