CBMS Conference: Elastic Functional and Shape Data Analysis (EFSDA)

(July 16,2018 - July 20,2018 )

Organizers


Sebastian Kurtek
Statistics, The Ohio State University
Facundo Memoli
Mathematics, The Ohio State University
Yusu Wang
Computer Science and Engineering, The Ohio State University
Tingting Zhang
Statistics, University of Virginia
Hongtu Zhu
Biostatistics, University of Texas MD Anderson Cancer Center

UPDATE!

Additional conference materials can be found at: https://www.asc.ohio-state.edu/kurtek.1/cbms.html

Topic Area

This Conference Board of the Mathematical Sciences (CBMS) conference will feature an intensive lecture series on elastic methods for statistical analysis of functional and shape data, using tools from Riemannian geometry, Hilbert space methods, and computational science. The main focus of this conference is on geometric approaches, especially on using elastic Riemannian metrics with desired invariance properties, and square-root representations that simplify computations. These approaches allow joint registration and statistical analysis of functional data, and are termed elastic for that reason. The statistical goals include comparisons, summarization, clustering, modeling, and testing of functional and shape data objects.

There is no travel/accomodation funding remaining, however we are still accepting applications to participate.

Travel and Lodging Info

  • Lodging - There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.
  • Airport - When you arrive at John Glenn Columbus International airport-CMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24-hour Airport taxi service.
  • Driving to MBI & Campus Parking - If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.

Primary Lecturer

Prof. Anuj Srivastava is a Professor of Statistics and a Distinguished Research Professor at Florida State University (FSU) in Tallahassee, FL. His main expertise lies in the use of techniques from algebra and differential geometry in deriving statistical inferences on nonlinear manifolds. Specifically, along with his colleagues, he has developed comprehensive Riemannian frameworks for shape analysis of objects, including scalar functions, Euclidean curves, 2D surfaces, and neuronal trees. He is an author, along with Prof. Eric Klassen of FSU, of a recently published Springer textbook on Functional and Shape Data Analysis. He has also published more than 200 papers in refereed journals and proceedings of refereed international conferences. He is a fellow of the IEEE, IAPR, and ASA.

Additional Lecturers

Prof. Eric Klassen, Department of Mathematics, Florida State University
Prof. Veera Baladandayuthapani, Department of Biostatistics, University of Texas MD Anderson Cancer Center
Prof. Laurent Younes, Department of Applied Mathematics and Statistics, Johns Hopkins University
Prof. Zhengwu Zhang, Department of Biostatistics and Computational Biology, University of Rochester

We gratefully acknowledge funding and support from the National Science Foundation CBMS grant, the Mathematics Research Institute, the Mathematical Biosciences Institute, the Department of Statistics at Ohio State, and the NSF TRIPODS grant.

Accepted Speakers

Veera Baladandayuthapani
Department of Biostatistics, UT MD Anderson Cancer Center
Eric Klassen
Mathematics, Florida State University
Anuj Srivastava
Statistics, Florida State University
Laurent Younes
Applied Mathematics and Statistics, Johns Hopkins University
Zhengwu Zhang
Department of Biostatistics and Computational Biology, University of Rochester
Monday, July 16, 2018
Time Session
08:30 AM
09:15 AM

Breakfast

09:15 AM
09:30 AM

Opening Remarks

09:30 AM
12:00 PM
Anuj Srivastava - Introduction and Background
  • Introduction and motivation.
  • Function Spaces: norms, Hilbert space; L2 metric; complete orthonormal basis; sample mean, sample covariance; functional Principal Component Analysis (fPCA); functional regression models; generative models for functional data; least squares curve fitting.
12:00 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM
Anuj Srivastava - Elastic Functional Data Analysis
  • Background from geometry and algebra: manifolds, Riemannian metric, geodesics, exponential and inverse exponential map, Karcher/Frechet means; functional spaces of interest: set of probability density functions (pdfs), set of warping functions, group, group actions, quotient spaces.
  • Phase variability and the registration problem; L2 metric and pinching problem; dynamic programming algorithm; penalized L2 metric.
  • Invariance, square-root velocity function (SRVF); Fisher-Rao Riemannian metric; change of variables; registration using SRVFs; exact solution and approximation; quotient space metric, amplitude and phase distances.
04:30 PM
06:30 PM

Reception

Tuesday, July 17, 2018
Time Session
08:45 AM
09:30 AM

Breakfast

09:30 AM
12:00 PM
Anuj Srivastava - Elastic Shape Analysis of Curves
  • Goals and motivation; Past approaches in shape analysis; shape-preserving group actions; Kendall's shape analysis; active shape models; registration problem; non-elastic framework.
  • Elastic Riemannian metric; SRVF; open curves and closed curves; shape geodesics.
  • Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
12:00 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM
Anuj Srivastava, Eric Klassen - Fundamental Mathematical Formulations, Recent Progress and Open Problems
  • scalar FDA
  • characterization of orbits
  • existence of optimal matching for piecewise-linear curves
  • C1 functions
04:30 PM
05:30 PM

Discussion Session

Wednesday, July 18, 2018
Time Session
08:45 AM
09:30 AM

Breakfast

09:30 AM
12:00 PM
Anuj Srivastava - Elastic Shape Analysis of Surfaces
  • Goals and motivation; past approaches; Iterative Closest Point (ICP) algorithm.
  • Representations of surfaces: coordinate functions, gradient field, surface normal, 1nd fundamental form, 2nd fundamental form.
  • Registration problem; elastic Riemannian metric; square-root normal fields (SRNFs); inversion problem; shape geodesics.
  • Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
12:00 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM
Anuj Srivastava, Karthik Bharath - Statistical Models
  • Statistical modeling of functional data: Karcher mean, multiple registration, fPCA in quotient space.
  • Curves on manifolds: smoothing splines.
  • Trajectories on Manifolds: issues; transported SRVFs, vector bundle representations, tangent bundle representation.
04:30 PM
05:30 PM

Software Demonstrations in Matlab

Thursday, July 19, 2018
Time Session
08:45 AM
09:30 AM

Breakfast

09:30 AM
12:00 PM
Eric Klassen, Anuj Srivastava - Generalizations of the Square Root Velocity Framework to Trajectories in Manifolds

In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM
Laurent Younes - Introduction to Metric Registration

Registration (for curves, surfaces or images) can be seen as a representation of a shape dataset as a subset of the diffeomorphism group, each shape in the dataset being associated with an optimal deformation of a template. We will in particular focus on methods that compute this deformation by optimizing a distance over diffeomorphisms under the constraint of mapping a template to a target, and such that the minimized distance is in turn a metric in shape space. These “metric registration” methods include a large spectrum of algorithms deriving from the “large deformation diffeomorphic metric mapping” (LDDMM) framework, and “metamorphosis” in which non-diffeomorphic shape variations are also allowed. We will describe mathematical foundations and algorithms, and the various forms that these methods may take in relation to applications.

04:30 PM
05:30 PM

Software Demonstrations in Matlab

Friday, July 20, 2018
Time Session
08:45 AM
09:30 AM

Breakfast

09:30 AM
12:00 PM
Veera Baladandayuthapani - Bayesian Models for Richly Structured Data in Biomedicine

Modern scientific endeavors generate high-throughput, multi-model datasets of different sizes, formats, and structures at a single subject-level. In the context of biomedicine, such data include multi-platform genomics, proteomics and imaging; and each of these distinct data types provides a different, partly independent and complementary, high-resolution view of various biological processes. Modeling and inference in such studies is challenging, not only due to high dimensionality, but also due to presence of rich structured dependencies such as serial, spatial, graphical, functional and shape-based correlations. This talk will cover probabilistic frameworks that acknowledge and exploit these inherent complex structural relationships to develop regression and clustering models, that extract maximal information from such data. These approaches will be illustrated using several biomedical case examples especially in oncology.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
04:00 PM
Zhengwu Zhang - Geometry-based Brain Structural Connectome Analysis

Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies non-invasively. The structural connectome is initially shaped by genetics and subsequently refined by the environment. It is extremely interesting to study structural connectomes and their relationships to environmental factors or human traits, which motivates the routine collection of high-resolution connectomes in large human studies (e.g., the Human Connectome Project and UK Biobank). However, there is a fundamental gap between the state of the art in image acquisition and the tools available to reconstruct and analyze the connectome data, due to the complexity of data. This lecture aims at introducing our recent effort in the thread. More specifically, we will introduce a population-based structural connectome (PSC) mapping framework to reproducibly extract binary networks, weighted networks, and streamline-based brain connectomes. In addition, various novel methods of analyzing the outputs of PSC will be introduced. We will also introduce a user-friendly software package that implements the PSC and the analysis methods.

04:00 PM
04:15 PM

Closing Remarks

Name Email Affiliation
Acharyya, Satwik satwik91@gmail.com Statistics, Texas A & M University
Baladandayuthapani, Veera veera@mdanderson.org Department of Biostatistics, UT MD Anderson Cancer Center
Benard, Efuelaka efuelaka@yahoo.com STATISTICS, UNIVERSITY OF HASSELT
Bharath, Karthik karthik.bharath@nottingham.ac.uk Mathematical Sciences, University of Nottingham
Chen, Chao cc16w@my.fsu.edu statistics, Florida State University
Cho, Min Ho cho.829@osu.edu Statistics,
Flaih, Ahmad ahmad.flaih@qu.edu.iq STATISTICS, UNIVERSITY OF AL-QADISIYAH
Guha, Aritra aritra@umich.edu Statistics, University of Michigan
Guo, Mengmeng mengmeng.guo@ttu.edu Mathematics, Texas Tech University
Honaker, John honaker.32@osu.edu Statistics, The Ohio State University
Hong, Yi hongyi.cs@gmail.com Computer Science, University of Georgia
Hu, Ziqing zhu4@nd.edu ACMS, University of Notre Dame
Kakareko, Sylwia sylwia.kakareko@gmail.com Industrial and Manufacturing Engineering, Florida State University
Kang, Hyun Bin hbkang0823@gmail.com Statistics, Pennsylvania State University
Kausar, Rukhsana rukhsana718@gmail.com Department of Mathematics, University of Kaiserslautern
Kim, Kyongwon kyongwon.psu@gmail.com Statistics, Pennsylvania State University
Klassen, Eric klassen@math.fsu.edu Mathematics, Florida State University
Kurtek, Sebastian kurtek.1@stat.osu.edu Statistics, The Ohio State University
Li, Huazhang hl5qd@virginia.edu Statistics, University of Virginia
Li, Tengfei tengfeili2006@gmail.com Biostatistics, University of Texas MD Anderson Cancer Center
Lu, Yi lu08stat@gmail.com Mathematics and Computer Science, Drew University
Maltsi, Anieza maltsi@wias-berlin.de PARTIAL DIFFERENTIAL EQUATIONS GROUP, Weierstrass-Institut f""ur Angewandte Analysis und Stochastik (WIAS)
Manley, Kevin kmanley1@nd.edu Applied and Computational Math and Statistics, University of Notre Dame
Matuk, James matuk.3@osu.edu Statistics, The Ohio State University
Memoli, Facundo memoli@math.osu.edu Mathematics, The Ohio State University
Miao, Ruizhong rm9dd@virginia.edu Statistics, University of Virginia
Mitchell, Emily emily.mitchell@nottingham.ac.uk Mathematical Sciences, University of Nottingham
Prematilake, Chalani prematilakec17@ecu.edu Mathematics, East Carolina University
Qadir, Ghulam ghulam.qadir@kaust.edu.sa Statistics, King Abdullah University of Science and Technology (KAUST)
Rao, Arvind ukarvind.cmu@gmail.com Bioinformatics, University of Michigan Health Systems
Ronquist, Scott scotronq@umich.edu Bioinformatics, University of Michigan
Rooks, Brian btrooks88@gmail.com Department of Biostatistics and Computational Biology, University of Rochester
Saha, Abhijoy saha.58@osu.edu Statistics, The Ohio State University
Shen, Luyi lshen4@nd.edu ACMS, University of Notre Dame
Shieh, Denise dshieh08@gmail.com Biostatistics, Columbia University
Shu, Hai hshu@mdanderson.org Biostatistics, University of Texas MD Anderson Cancer Center
Soto, Carlos cjs15g@my.fsu.edu Statistics, Florida State University
Srivastava, Anuj anuj@stat.fsu.edu Statistics, Florida State University
Strait, Justin strait.50@osu.edu Statistics, The Ohio State University
Wang, Yusu yusu@cse.ohio-state.edu Computer Science and Engineering, The Ohio State University
Wang, Yuan yuan.wang.stat@gmail.com Mathematics and Statistics, Washington State University
Wang, Boshi boshiwang1993@gmail.com Department of statistics, Florida State University
Wang, Xuan wangxuan209@hotmail.com mathematics, Zhejiang University
Younes, Laurent laurent.younes@jhu.edu Applied Mathematics and Statistics, Johns Hopkins University
Zhang, Tingting tz3b@virginia.edu Statistics, University of Virginia
Zhang, Zhengwu zhengwu_zhang@urmc.rochester.edu Department of Biostatistics and Computational Biology, University of Rochester
Zhang, Jian-Zhou zhangjz@scu.edu.cn College of Computer, Sichuan University
Zohner, Ye Emma emma.zohner@rice.edu Biostatistics, MD Anderson Cancer Center
Bayesian Models for Richly Structured Data in Biomedicine

Modern scientific endeavors generate high-throughput, multi-model datasets of different sizes, formats, and structures at a single subject-level. In the context of biomedicine, such data include multi-platform genomics, proteomics and imaging; and each of these distinct data types provides a different, partly independent and complementary, high-resolution view of various biological processes. Modeling and inference in such studies is challenging, not only due to high dimensionality, but also due to presence of rich structured dependencies such as serial, spatial, graphical, functional and shape-based correlations. This talk will cover probabilistic frameworks that acknowledge and exploit these inherent complex structural relationships to develop regression and clustering models, that extract maximal information from such data. These approaches will be illustrated using several biomedical case examples especially in oncology.

Statistical Models
  • Statistical modeling of functional data: Karcher mean, multiple registration, fPCA in quotient space.
  • Curves on manifolds: smoothing splines.
  • Trajectories on Manifolds: issues; transported SRVFs, vector bundle representations, tangent bundle representation.
Generalizations of the Square Root Velocity Framework to Trajectories in Manifolds

In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.

Fundamental Mathematical Formulations, Recent Progress and Open Problems
  • scalar FDA
  • characterization of orbits
  • existence of optimal matching for piecewise-linear curves
  • C1 functions
Generalizations of the Square Root Velocity Framework to Trajectories in Manifolds

In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.

Introduction and Background
  • Introduction and motivation.
  • Function Spaces: norms, Hilbert space; L2 metric; complete orthonormal basis; sample mean, sample covariance; functional Principal Component Analysis (fPCA); functional regression models; generative models for functional data; least squares curve fitting.
Elastic Functional Data Analysis
  • Background from geometry and algebra: manifolds, Riemannian metric, geodesics, exponential and inverse exponential map, Karcher/Frechet means; functional spaces of interest: set of probability density functions (pdfs), set of warping functions, group, group actions, quotient spaces.
  • Phase variability and the registration problem; L2 metric and pinching problem; dynamic programming algorithm; penalized L2 metric.
  • Invariance, square-root velocity function (SRVF); Fisher-Rao Riemannian metric; change of variables; registration using SRVFs; exact solution and approximation; quotient space metric, amplitude and phase distances.
Elastic Shape Analysis of Curves
  • Goals and motivation; Past approaches in shape analysis; shape-preserving group actions; Kendall's shape analysis; active shape models; registration problem; non-elastic framework.
  • Elastic Riemannian metric; SRVF; open curves and closed curves; shape geodesics.
  • Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
Fundamental Mathematical Formulations, Recent Progress and Open Problems
  • scalar FDA
  • characterization of orbits
  • existence of optimal matching for piecewise-linear curves
  • C1 functions
Elastic Shape Analysis of Surfaces
  • Goals and motivation; past approaches; Iterative Closest Point (ICP) algorithm.
  • Representations of surfaces: coordinate functions, gradient field, surface normal, 1nd fundamental form, 2nd fundamental form.
  • Registration problem; elastic Riemannian metric; square-root normal fields (SRNFs); inversion problem; shape geodesics.
  • Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
Statistical Models
  • Statistical modeling of functional data: Karcher mean, multiple registration, fPCA in quotient space.
  • Curves on manifolds: smoothing splines.
  • Trajectories on Manifolds: issues; transported SRVFs, vector bundle representations, tangent bundle representation.
Introduction to Metric Registration

Registration (for curves, surfaces or images) can be seen as a representation of a shape dataset as a subset of the diffeomorphism group, each shape in the dataset being associated with an optimal deformation of a template. We will in particular focus on methods that compute this deformation by optimizing a distance over diffeomorphisms under the constraint of mapping a template to a target, and such that the minimized distance is in turn a metric in shape space. These “metric registration” methods include a large spectrum of algorithms deriving from the “large deformation diffeomorphic metric mapping” (LDDMM) framework, and “metamorphosis” in which non-diffeomorphic shape variations are also allowed. We will describe mathematical foundations and algorithms, and the various forms that these methods may take in relation to applications.

Geometry-based Brain Structural Connectome Analysis

Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies non-invasively. The structural connectome is initially shaped by genetics and subsequently refined by the environment. It is extremely interesting to study structural connectomes and their relationships to environmental factors or human traits, which motivates the routine collection of high-resolution connectomes in large human studies (e.g., the Human Connectome Project and UK Biobank). However, there is a fundamental gap between the state of the art in image acquisition and the tools available to reconstruct and analyze the connectome data, due to the complexity of data. This lecture aims at introducing our recent effort in the thread. More specifically, we will introduce a population-based structural connectome (PSC) mapping framework to reproducibly extract binary networks, weighted networks, and streamline-based brain connectomes. In addition, various novel methods of analyzing the outputs of PSC will be introduced. We will also introduce a user-friendly software package that implements the PSC and the analysis methods.

video image

Introduction and Background
Anuj Srivastava

  • Introduction and motivation.
  • Function Spaces: norms, Hilbert space; L2 metric; complete orthonormal basis; sample mean, sample covariance; functional Principal Component Analysis (fPCA); functional regression m