Topological Data Analysis

Description

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In this age of rapidly increasing access to ever larger data sets, it has become clear that studying the “shape” of data using the tools of combinatorial and algebraic topology can lead to much deeper insights than other standard methods when analyzing complex data sets. Topological data analysis (TDA) is the exciting and highly active new field of research that encompasses these productive developments at the interface of algebraic topology, statistics, and data science. This workshop will consist of a small number of plenary one-hour lectures by leading researchers in the field, a larger number of contributed short talks from early-career researchers, live demos of software, a problem session, and a poster session. The speakers will cover a wide range of topics, from theory to concrete applications of TDA in science and engineering. The goals of the workshop are to foster scientific interactions across the growing breadth of the applied topology community and to provide an opportunity for algebraic topologists, statisticians, and data scientists curious about this dynamic new field to learn more about it.

Organizers

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B F
Brittany Fasy Mathematics
Montana State University
K H
Kathryn Hess Mathematics
EPFL
M K
Matthew Kahle Mathematics
Ohio State University
S M
Sayan Mukherjee Statistics
Duke University
J P
Jose Perea Mathematics
Michigan State University

Invited Speakers

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L C
Lorin Crawford Microsoft Research New England
S K
Sara Kalisnik Bentley University
F M
Facundo Memoli Ohio State
E M
Ezra Miller Duke University
A M
Anthea Monod Imperial College London
E M
Elizabeth Munch Michigan State University
V N
Vidit Nanda University of Oxford
K T
Katharine Turner Australian National University
Y W
Yusu Wang University of California, San Diego

Schedule

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Monday, April 26, 2021
9:00-9:50 CDT
Algebraic Wasserstein distance between persistence modules

Speaker: Katharine Turner (Australian National University)

10:15-10:45 CDT
From Geometry to Topology: Inverse Theorems for Distributed Persistence

Speaker: Elchanan Solomon (Duke University)

11:00-11:30 CDT
Ephemeral persistence modules and distance comparison

Speaker: Nicholas Berkouk (Ecole Polytechnique Fédérale de Lausanne)

13:00-13:50 CDT
Discrete Morse-based graph reconstruction and data analysis

Speaker: Yusu Wang (University of California, San Diego)

14:15-14:45 CDT
A simplicial extension of node2vec

Speaker: Celia Hacker (Ecole Polytechnique Fédérale de Lausanne)

15:00-15:30 CDT
Sketching Merge Trees

Speaker: Bei Wang (University of Utah)

Tuesday, April 27, 2021
9:00-9:50 CDT
Statistical Frameworks for Mapping 3D Shape Variation onto Genotypic and Phenotypic Variation

Speaker: Lorin Crawford (Microsoft Research)

10:15-10:45 CDT
Interleaving by parts for persistence in a poset

Speaker: Woojin Kim (Duke University)

11:00-11:30 CDT
Algebraic topology in the mesoscopic regime

Speaker: Antonio Rieser  (CONACYT-CIMAT, A.C.)

13:00-13:50 CDT
The Truncated Interleaving Distance for Reeb Graphs

Speaker: Elizabeth Munch (Michigan State University)

Wednesday, April 28, 2021
9:00-9:50 CDT
Curvature sets over persistence diagrams

Speaker: Facundo Memoli (Ohio State University)

10:15-10:45 CDT
Intrinsic Persistent Homology via density-based metric learning

Speaker: Ximena Fernández (Swansea University)

11:00-11:30 CDT
Approximate and discrete vector bundles

Speaker: Luis Scoccola  (Michigan State University)

13:00-13:50 CDT
Topological Data Analysis of Database Representations for Information Retrieval

Speaker: Anthea Monod (Imperial College)

14:15-14:45 CDT
Predicting Survival Outcomes using Topological Shape Features of AI-reconstructed Medical Images

Speaker: Chul Moon (Southern Methodist University)

Thursday, April 29, 2021
9:15-9:45 CDT
Back to Basics – Topology of Simplicial Complexes for Business Optimisations

Speaker: Marc Lange (Elbformat Consulting)

10:15-10:45 CDT
Learning with Approximate or Distributed Topology

Speaker: Alexander Wagner (Duke University)

11:00-11:30 CDT
Geometric and Topological Fingerprints for Periodic Crystals

Speaker: Teresa Heiss (Institute of Science and Technology Austria)

13:00-13:50 CDT
Sampling smooth manifolds using ellipsoids

Speaker: Sara Kalisnik (Bentley University)

14:15-14:45 CDT
Simplicial Neural Networks

Speaker: Stefania Ebli  (Ecole Polytechnique Fédérale de Lausanne)

15:00-15:30 CDT
Topological Sholl Descriptors for Neuronal Clustering and Classification

Speaker: Sadok Kallel (American University of Sharjah)

Friday, April 30, 2021
9:00-9:50 CDT
Compatibility and Optimization for Quiver Representations

Speaker: Vidit Nanda (University of Oxford)

10:15-10:45 CDT
The amplitude of an abelian category: Measures in persistence theory

Speaker: Barbara Giunti (Technische Universität Graz)

11:00-11:30 CDT
Sliding windows persistence of quasiperiodic functions

Speaker: Hitesh Gakhar (University of Oklahoma)

13:00-13:50 CDT
What are left and right endpoints for multiparameter persistence?

Speaker: Ezra Miller (Duke University)

14:15-14:45 CDT
Identifying analogous topological features across multiple systems

Speaker: Iris Yoon (University of Delaware)

15:00-15:30 CDT
Recent Advances in Topology-Based Graph Classification

Speaker: Bastian Rieck (ETH Zurich)


Poster Directory

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PresenterTitle
Mehmet Emin Aktas (University of Central Oklahoma)Two New Hypergraph Laplacians in Diffusion Framework
Erik J Amezquita (Michigan State University)Using topology to analyze the shape of barley
Aras Asaad (Oxford Drug Design)Persistent Homology to Detect Fake Faces and Videos
Tahmineh Azizi (Kansas State University)Topological Patterns in Ecology
Rituparna Basak (New Jersey Institute of Technology)Application of computational topology to analysis of granular material force networks in the stick-slip regime
Håvard Bakke Bjerkevik (TU Graz)$ell^p$-Distances on Multiparameter Persistence Modules
Elyse Borgert (University of North Carolina Chapel Hill)Persistent topology of protein space
Chao Cheng (New Jersey Institute of Technology)Insight from topological data analysis into precursors to stick-slip events in sheared granular systems
Veronica Ciocanel (Duke University)TDA for biological ring channels
Pedro Conceicao (University of Aberdeen)An application of neighbourhoods in digraphs to the classification of binary dynamics
Justin M Curry (SUNY Albany)Decorated Merge Trees for Persistent Topology
Russell J Funk (University of Minnesota, Twin Cities)The Emergence of Higher-Order Structure in Scientific and Technological Knowledge Networks
Jehan Ghafuri (The University of Buckingham)Sensitivity and stability of pretrained CNN filters
Golnar G Gharooni Fard (University of Colorado, Boulder)A Persistent Homology Approach for Characterizing Honeybee Behavior during Food Exchange
Sayonita Ghosh Hajra (California State University, Sacramento (CSU Sacramento))Topological shapes of election speeches
Mario R Gomez Flores (Ohio State University)Computational Aspects of Persistence Sets
İsmail Güzel (İstanbul Technical University)Hierarchical Clustering and Zeroth Persistent Homology
Niklas Hellmer (Polish Academy of Sciences)A Discrete Prokhorov Metric for Persistence Diagrams
Paul Samuel Ignacio (University of the Philippines Baguio)LUMÁWIG: A bypass approach to bottleneck distance
Péguy Kem-Meka Tiotsop Kadzue (Academia Avance)Topological Data Analysis : ToMATo Clustering
Miroslav Kramar (University of Oklahoma)Towards Understanding Complex Spatio-Temporal Systems
Darrick Lee (University of Pennsylvania)Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams
Elise McMahon (Glaxosmithkline, Cornell University)Using Mapper to Represent Biological Changes in a Cell
Nikola Milicevic (University of Florida, Gainesville)Applied Topology Using Cech’s Closure Spaces
Senthil Mudaliar (US Army)Saving lives in Multi-Organ Failure: We need a method to improve clinical decisions in real-time
Arnur Nigmetov (Lawrence Berkeley National Laboratory)Topological Regularization via Persistence-Sensitive Optimization
Miguel O’Malley (Wesleyan University)(Persistent) Magnitude and Data
Matt Piekenbrock (Michigan State University)Fast persistence computations in sparse dynamic settings
Brenda L Praggastis (Pacific Northwest National Laboratory (PNNL))Deep Data Profiler: A Platform and Methodology for the Analysis and Interpretation of Neural Networks
Yu Qin (Tulane University)Comparing Distance Metrics on Vectorized Persistence Summaries
Alexander Rolle (TU Graz)Multi-parameter persistence, clustering, and density estimation
Benjamin Roycraft (University of California Davis)Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics
Alexander D Smith (University of Wisconsin, Madison)Topological Data Analysis: Applications in Molecular Simulation
Francesca Tombari (KTH)Homotopical decompositions of simplicial and Vietoris-Rips complexes
Josué Tonelli-Cueto (Inria Paris & IMJ-PRG)Computing the Homology of Semialgebraic Sets via TDA
Álvaro Torras CasasPersistence Spectral Sequences: Applications and Stability
Renata TurkesNoise robustness of persistent homology on greyscale images across filtrations and signatures
Mikael Vejdemo-JohanssonMultiple Hypothesis Testing with Persistent Homology
Siddharth VishwanathRobust Persistence Diagrams using Reproducing Kernels
Milton Chi-Chong WongPersFormer: A Transformer Model for Persistence Diagrams
Min-Chun WuA topological approach to inferring the intrinsic dimension of convex sensing data
Ling ZhouPersistent homotopy groups of metric spaces

Videos

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Algebraic Wasserstein distance between persistence modules

Katharine Turner
April 26, 2021

From Geometry to Topology: Inverse Theorems for Distributed Persistence

Elchanan Solomon
April 26, 2021

Ephemeral persistence modules and distance comparison

Nicholas Berkouk
April 26, 2021

Discrete Morse-based graph reconstruction and data analysis

Yusu Wang
April 26, 2021

A simplicial extension of node2vec

Celia Hacker
April 26, 2021

Sketching Merge Trees

Bei Wang
April 26, 2021

Statistical Frameworks for Mapping 3D Shape Variation onto Genotypic and Phenotypic Variation

Lorin Crawford
April 27, 2021

Interleaving by parts for persistence in a poset

Woojin Kim
April 27, 2021

Algebraic topology in the mesoscopic regime

Antonio Rieser 
April 27, 2021

The Truncated Interleaving Distance for Reeb Graphs

Elizabeth Munch
April 27, 2021

Curvature sets over persistence diagrams

Facundo Memoli
April 28, 2021

Intrinsic Persistent Homology via density-based metric learning

Ximena Fernández
April 28, 2021

Approximate and discrete vector bundles

Luis Scoccola 
April 28, 2021

Topological Data Analysis of Database Representations for Information Retrieval

Anthea Monod
April 28, 2021

Predicting Survival Outcomes using Topological Shape Features of AI-reconstructed Medical Images

Chul Moon
April 28, 2021

Back to Basics – Topology of Simplicial Complexes for Business Optimisations

Marc Lange
April 29, 2021

Learning with Approximate or Distributed Topology

Alexander Wagner
April 29, 2021

Geometric and Topological Fingerprints for Periodic Crystals

Teresa Heiss
April 29, 2021

Simplicial Neural Networks

Stefania Ebli 
April 29, 2021

Topological Sholl Descriptors for Neuronal Clustering and Classification

Sadok Kallel
April 29, 2021

Compatibility and Optimization for Quiver Representations

Vidit Nanda
April 30, 2021

The amplitude of an abelian category: Measures in persistence theory

Barbara Giunti
April 30, 2021

Sliding windows persistence of quasiperiodic functions

Hitesh Gakhar
April 30, 2021

What are left and right endpoints for multiparameter persistence?

Ezra Miller
April 30, 2021

Identifying analogous topological features across multiple systems

Iris Yoon
April 30, 2021

Recent Advances in Topology-Based Graph Classification

Bastian Rieck
April 30, 2021

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