SC.07 Topological and Object Oriented Data Analysis

Sunday, 5 July 2020  |  9:00 - 17:00 | Location: TBD

  • James Steve Marron, UNC Chapel Hill
  • Yuan Wang, University of Wisconsin-Madison
  • Moo K. Chung, University of South Carolina
Course Web-page:


The era of big data in biology and medicine brings exciting opportunities for new scientific discoveries and new challenges for biostatistics. Yet, valuable information in the sheer amount of complex data may be hidden in patterns that cannot be decoded easily with standard statistical tools. The emerging area of topological data analysis (TDA) is a promising avenue of research to answer the challenge. TDA characterizes topological changes of multivariate representations of data in multidimensional scales. Not only does TDA reveal topological features in data only visible on a multi-scale level, the fact that overall topological changes hold more significance in TDA summary statistics over fleeting structures also makes the approach particularly robust at the presence of noise and artifacts. The unique powers of TDA are demonstrated by a decade worth of theory development and applications in computer vision, engineering, and neuroimaging. TDA has also provided tools for solving deep challenges in object-oriented data analysis (OODA), where the focus is in analyzing complex heterogeneous data. This short course is aimed at popularizing the state-of-the-art in TDA computation and methodology with detailed illustration using real datasets coming from medical imaging studies and genetics. 


Participants will benefit the most from the course if they have prior knowledge in linear algebra, calculus, and basic statistics (estimation, inference, regression, multivariate analysis). 

Learning Outcomes:

Participants are expected to achieve the following learning outcomes at the end of the course:

  • Understand the basic concepts and principles of OODA and TDA. 
  • Understand appropriate statistical procedures and approaches for OODA and TDA. 
  • Begin to apply OODA and TDA concepts and procedures to complex real-world data using the distributed R and MATLAB codes

Course Syllabus

Three leading experts in Object Oriented Data Analysis (OODA) and Topological Data Analysis (TDA) will give the full day course. Each expert will give a 2-hour lecture split into two 1 hour sessions. The first secession will be on theory and the second session will be on applications and R/MATLAB demonstration. 

Session 1-1. Introduction to Object Oriented Data Analysis (OODA). Marron will introduce the basic concepts and theory of OODA. 

Session 1-2. Application of OODA. Marron will explain how the OODA principles can be used in analyzing complex real-world data, e.g., analysis of the variation in populations of tree-structured objects, such as brain arteries, forming a non-Euclidean space. R/MATLAB demonstration will be given. 

Session 2-1. Introduction to Topological Data Analysis (TDA). Wang will introduce the key TDA concepts and technique persistent homology (PH) through point cloud data and simplicial complex, and demonstrate the standard algorithm for computing filtration and standard PH features (barcodes, persistence diagram, persistence landscape). 

Session 2-2. Topological Signal Processing. Wang will give a tutorial on applying PH to various time series data such as electroencephalographic (EEG) signals, functional magnetic resonance imaging (fMRI) signals, and audial signals, and designing appropriate statistical test for PH features in these settings. R/MATLAB demonstration will be given. 

Session 3-1. TDA and OODA on heterogeneous data such as graphs and networks. Chung will introduce the key theoretical concepts and modeling principles on heterogeneous data.

Session 3-2. Chung will give a tutorial on analyzing various heterogeneous data from real-world examples including social networks, brain networks and SNP-networks coming from genome-wide association studies. R/MATLAB demonstration will be given. 


A self-contained textbook will be made available for download on the course webpage before the workshop.


R and MATLAB codes will be made available for download on the course webpage before the workshop. Participants are encouraged to bring their own laptop for implementing the codes during the hands-on demonstration.

About the Instructors:
James Steve Marron is Amos Hawley Professor of Statistics and Operations Research at University of North Carolina at Chapel Hill. Marron is a leading expert on Object Oriented Data Analysis and has published numerous papers on the topic and regularly teaches the graduate courses on this topic: Marron is currently writing a book of the same title with Ian L. Dryden:


Moo K. Chung is an Associate Professor of Biostatistics and Medical Informatics at University of Wisconsin-Madison. Chung is a leading expert of Topological Data analysis and has published more than 20 peer reviewed papers on this topic.  Chung has written two books, where many chapters are devoted to this topic, through World Scientific Press: and Cambridge University Press Chung provided numerous tutorials on the topic in KAUST and INRIA among other places. The topic is regularly taught in the graduate course he is teaching every year:

Yuan Wang
 is an Assistant Professor of Biostatistics at the University of South Carolina. Wang is a leading expert on Topological Data Analysis in signal processing, particularly in electroencephalographic signals. She has published five peer-reviewed papers on this topic including a recent publication Annals of Applied Statistics on this topic: She has recently taught a two-hour tutorial on Topological Signal Processing and Network Analysis at KAUST.