Instructor: Dr. Bei Wang Phillips (beiwang AT sci.utah.edu)
Lectures: Tuesdays, Thursdays, 9:10am - 10:30am, IVC via Zoom
Tuesdays 10:30 am - 11:30 am or by appointment (beiwang AT sci.utah.edu), office hours via Zoom
Computational topology is at the intersection of algebraic topology and computer science.
It serves as the foundation for Topological Data Analysis (TDA).
TDA is an emerging area in exploratory data analysis and data mining. It has had growing interests and notable successes with an expanding research community. The application of topological techniques to large and complex data has opened up new opportunities in science, engineering and business intelligence. The goal of TDA is to understand complex datasets, where complexity arises from not only the massiveness of the data but also from the richness of the features. The objective of this class is to enable the students to become familiar with these new methods in computational topology and TDA, from theory, algorithm and application perspectives.
Successful completion of the course will enable the students to become data practitioners who can apply TDA pipelines to a variety of real-world datasets in material science, biomedicine, business intelligence, etc. The students can also pursue new research directions in the field of computational topology and TDA, as well as integrate advanced TDA techniques with other areas of data science such as data mining, machine learning, 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, in particular, from Computer Science and Mathematics.
The students are not required to be majoring in Computer Science or Mathematics, 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.
The course materials are organized under three mutually inclusive modules:
The course may cover (but is not limited to) the following topics:
- TDA Foundations and Pipeline (FP)
- TDA, Machine Learning and Statistics (ML)
- TDA in Data Science (DS)
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.
- 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)
- Practical applications of TDA
Most communication is handled through the Canvas system. Additionally, please feel free to email the instructor for questions.
When class material questions are sent to the instructor, we may isolate the question and post the response to Canvas (so that all can learn from both the question and the answer).
Computational Topology: An Introduction by Herbert Edelsbrunner and John Harer
The University of Utah seeks to provide equal access to its
programs, services and activities for people with disabilities.
you will need accommodations in the class, reasonable prior notice
to be given to the Center for Disability Services, 162 Olpin Union
581-5020 (V/TDD). CDS will work with you and the instructor to
arrangements for accommodations.
All written information in this course can be made available in
format with prior notification to the Center for Disability Services.