CS 6170: Computational Topology

Topological Data Analysis: The New Frontier of Data Science

Spring 2017


Instructor: Bei Wang Phillips (beiwang AT sci.utah.edu, WEB 4608)

TA: Sourabh Palande (sourabh AT sci.utah.edu, WEB 4750)

Lectures: Tuesdays, Thursdays, 9:10am - 10:30am, WEB L120

Office Hours:

  Bei Wang Phillips: Tuesdays 10:30 am - 11:30 am or by appointment (beiwang AT sci.utah.edu), WEB 4608

  Sourabh Palande: Wednesdays 1:00 pm - 3:00 pm and Thursdays 10:30 am - 12:00 pm or by appointment (sourabh AT sci.utah.edu), MEB 3115

Course Description: Topological Data Analysis (TDA) is an emerging area in exploratory data analysis and data mining. It has had a growing interests and notable successes with an expanding research community. The application of topological techniques to traditional data analysis has opened up new opportunities beyond just the statistical settings. The goal of TDA is to understand complex datasets, where complexity arises from not only the massiveness of the data, but also from richness of the features. The objective of this class is to enable the students to become familiar with these new methods in TDA, from theory, algorithm and application perspectives.

The course is going to focus roughly 1/3 on theory, 2/3 on practice (1/3 practical algorithms and 1/3 applications), with the data domain including material science, combustion simulation, biology, marketing, etc.

Successful completion of the course will enable the students to pursue new research directions in the field of TDA and/or apply the most recent topological techniques to related areas such as data analysis, computer graphics, geometric modeling, mesh generation, and data visualization.

Prerequisites: There are no formal prerequisites for this class. Students will be expected to have basic knowledge of data structures and algorithmic techniques.

The targeted audience for the class includes PhD students, mater students and very-motivated upper level undergraduate students. The students are not required to be majoring in Computer Science, but it is preferable that the students have some background in algorithms and/or other data science related courses. (If you are not sure whether you are qualified to take this class, please email the instructor.)

Suggested Topics: The course will cover (but is not limited to) the following topics:

  • Basic concepts (graphs, connected components, topological space, manifold, point cloud samples)
  • Combinatorial structures on point cloud data (simplicial complexes)
  • New techniques in dimension reduction (circular coordinates, etc.)
  • Clustering (topology-based data partition, classification)
  • Homology and persistent homology
  • Topological signatures for classification
  • Structural inference and reconstruction from data
  • Topological algorithms for massive data
  • Multivariate and high-dimensional data analysis
  • Topological data analysis for visualization (vector fields, topological structures)
Assignments: The students will be given individual and group assignments. The main assignment will be a course project. A list of project ideas will be provided, and the students are encouraged to propose project ideas and discuss them with the instructor. Students are allowed to work in small groups for large projects.

Class Information:

Communication: Most communication is handled through the Canvas system. Additionally, please feel free to email the TA and the instructor for questions. When class material questions are sent to the instructor or the TA, we may isolate the question and post the response to Canvas (so that all can learn from both the question and answer).


Required Textbook:

Computational Topology: An Introduction by Herbert Edelsbrunner and John Harer


Recommended Reading:

Disability Notice

The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities.  If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD).  CDS will work with you and the instructor to make arrangements for accommodations.

All written information in this course can be made available in alternative format with prior notification to the Center for Disability Services.