2013-14: LDHD: Topological Data Analysis: February 3-7, 2014

Location

This workshop was held at SAMSI.

Description

Topological Data Analysis began a little more than 20 years ago with the introduction of persistence by Edelsbrunner, Lestcher and Zomorodian. Since that time the field has grown significantly. Many strong theorems, numerous algorithms, and pieces of software have been created in that period. More recently, the field has considered stochastic modeling and analysis, which has resulted in interactions with Statistics, Probability, and Computer Science. This workshop focused on the interaction of Statistics and Probability with this new area of Applied Mathematics. The goals were to familiarize people in both areas with techniques from the other and to understand what future directions are the most promising.

Topics included:

  • Statistics and persistent homology
  • Topological data analysis and inference in dynamical systems and time series
  • Topological data analysis and shape statistics
  • Topological data analysis and network models
  • Probability models for random topology objects
  • Statistical applications of Hodge theory

Schedule and Supporting Media

Participant List
Speaker Title and Abstracts
Poster Titles

Monday, February 3, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
8:30-8:55 Registration
8:55-9:00 Welcome
9:00-9:40 Stability and Convergence Properties of Persistence Diagrams in Topological Data Analysis Frederic Chazal, INRIA
9:40-10:00 Break
10:00-10:40 Data Sparsification in Inferring Topology of Manifolds Yusu Wang, Ohio State University
10:40-11:00 Break
11:00-11:40 Statistical Topological Data Analysis using Persistence Landscapes Peter Bubenik, Cleveland State University pdf
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Mean and Variance of Metric Trees Megan Owen, Lehman College (CUNY)
1:40-2:00 Break
2:00-2:40 Some Uniformity Results for Dynamical Systems Andrew Nobel, University of North Carolina
2:40-3:00 Break
3:00-3:40 Statistical Inference for Functional Summaries of Persistent Homology Larry Wasserman, Carnegie Mellon University
3:40-4:00 Break
4:00-5:00 Discussion

Tuesday, February 4, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-9:40 What is the Dimension of the Internet? Yuliy Baryshnikov, University of Illinois
9:40-10:00 Break
10:00-10:40 Can Topological Summary Statistics be Sufficient? Katharine Turner, University of Chicago pdf
10:40-11:00 Break
11:00-11:40 Topological and Statistical Data Analysis Giseon Heo, University of Alberta pdf
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Curvature Sets over Persistence Diagrams Facundo Memoli, Ohio State University
1:40-2:00 Break
2:00-2:40 Persistent Local Homology: Theory, Algorithms, Applications, New Directions Paul Bendich, Duke University pdf
2:40-3:00 Break
3:00-3:40 Hodge Theory in Data Analysis Lek-Heng Lim, University of Chicago pdf
3:40-4:00 Break
4:00-5:00 Discussion
5:00-6:30 Poster Session and Reception

Wednesday, February 5, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-9:40 Statistical Inference for Persistence Diagrams Fabrizio Lecci, Carnegie Mellon University pdf
9:40-10:00 Break
10:00-10:40 Categorification of Reeb Graphs Elizabeth Munch, Institute for Mathematics and its Applications pdf
10:40-11:00 Break
11:00-11:40 OODA of Tree-Structured Data Objects J.S. Marron, University of North Carolina pdf
11:40-12:00 Discussion
12:00 Box Lunch (provided at SAMSI) – Free Afternoon

Thursday, February 6, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-9:40 Persistent Homology of Time-delay Embeddings Jose Perea, Duke University
9:40-10:00 Break
10:00-10:40 Persistent Homology of the Intergalactic Medium via the Lyman-alpha Forest Jessi Cisewski, Carnegie Mellon University
10:40-11:00 Break
11:00-11:40 Geometric Inference on Kernel Density Estimates Bei Wang, University of Utah pdf
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Local Homology Based Distance Between Maps Brittany Fasy, Tulane University pdf
1:40-2:00 Break
2:00-2:40 Distributed Homology using Harmonics Harish Chintakunta, North Carolina State University pdf
2:40-3:00 Break
3:00-3:40 Neighborhood Hypothesis Testing for Mean Contour Shapes of Corpus Callosum Mid Sections Vic Patrangenaru, Florida State University
3:40-4:00 Break
4:00-5:00 Discussion

Friday, February 7, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-9:40 Phase Transitions in Random Čech Complexes Omer Bobrowski, Duke University
9:40-10:00 Break
10:00-10:40 Quantifying Coverage in Dynamic Sensor Networks with Zigzag Persistent Homology Jennifer Gamble, North Carolina State University pdf
10:40-11:00 Break
11:00-11:40 Pyrosequencing and Computational Topology: A tale of two homologies Peter Kim, University of Guelph pdf
11:40-12:00 Discussion
12:00 Lunch (provided at SAMSI)
Adjourn