DSCI 475 - Topological Data Analysis

Time and Location: Mar 24 - May 18

• Tuesday and Thursday 9:30am-10:45am in Clark C 361

• Friday 10:00am-10:50am in Clark C 361

Office Hours: Thursday 11:00am-11:50am in Weber 218

[Syllabus]

Tentative Schedule:

Week 1:

Lecture: Course overview and introduction to topological data analysis [Slides]

Lab 1: Python setup and introduction to Python, NumPy, and Scikit-Learn [Supplementary: Introduction to Python Notebook] 

• [Lab 1 NumPy Tutorial], [Lab 1 Scikit-Learn Tutorial]

• [Lab 1 Problems]

  • [Lab 1 Solutions]

Week 2:

Lecture: Graph Theory and Simplicial Complexes [Week 2 Notes]

• [Homework 1] Due in class April 11

  • [Homework 1 Solutions]

• [Python Tutorial: Graph Laplacians and Betti Numbers in Python]

Week 3:

Lecture: Manifold Learning: Isomap [Week 3 Notes]

Lab 3: Isomap in Python

• [Lab 3 Tutorial]

• [Lab 3 Problems]

  • [Lab 3 Solutions]

Week 4:

Lecture: Data Visualization using Topology: Reeb Graphs and Mapper [Week 4 Slides]

Lab 4: Mapper in Python

• [Lab 4 Tutorial]

• [Lab 4 Problems]

Week 5:

Lecture: Persistent homology: Introduction [Week 5 Notes]

• [Homework 2] Due in class May 2

• [Supplementary: The Reduction Algorithm for Persistence]

Week 6:

Lecture: Persistence landscapes and persistence images [Week 6 Notes]

Lab 6: Persistence landscapes/images in Python

Week 7:

Lecture: Persistence and machine learning [Week 7 Notes]

Lab 7: Using persistence for dimensionality reduction, classification, and more with Python

Week 8: Final presentations, in Clark C 361 (the usual classroom) [Final Project Guidlines]

Tuesday May 13: Work on projects

Thursday May 15, 9:30am-10:45am: Final presentations

Friday May 16, 10-10:50am: Final presentations