CS 410/510: Topological Methods in Data Analysis and Machine Learning

Course Information:

Instructor:

Course Description:

This course is on the emerging field of topological data analysis (TDA) with an emphasis on applications for the practical purposes of data analysis. A core technique covered is Persistent Homology, which is a major tool driving the advancement of TDA. If time permits, more techniques such as Mapper, Merge Trees, or Reeb Graphs will also be covered. Since machine learning is a key application aimed by the course, part of the teaching is devoted to the necessary fundamental concepts for machine learning, given that students are not assumed to have known machine learning already. How to make use of the mainstream libraries in TDA (in our case, Gudhi) will also be taught.

TDA is about capturing the “global shape of data” that is meaningful in practice (after all, that’s what topology is good at). To make the course more accessible, key notions in topology (such as homology) are only taught in an “intuitive” way with the excessive mathematical formality intentionally suppressed. The goal is to motivate robust applications while still maintaining the soundness and solidness in understanding the key topological concepts for driving the applications. To that end, certain important concepts at the core of applications, which are sometimes implicitly assumed to be true, are explicitly laid out in this course.

Textbook:

Baris Coskunuzer and Cüneyt Gürcan Akçora. Topological Methods in Machine Learning: A Tutorial for Practitioners

Grading:

Assignments (35%), Final Project (60%), Participation (5%)

* Assignments and project instructions will be posted on Canvas

Course Announcements:

Other than directly stating things in class, I shall also announce important issues regarding the course through emails (automatically sent to the whole class through Canvas). So keep an eye on your UO email box.

Topics and Slides:

* An up-to-date schedule is maintained on Canvas
* Slides may be updated as teaching progresses
* We will be having Prof. Hank Childs giving us a guest lecture, most probably in the late half of the term (date TBD)
* Acknowledgment

More Resources:

* You can find much more by google searching yourself