DSCI 475 - Topological Data Analysis

Time and Location: MW 10:00am-10:50am, March 20 - May 10, in Forestry Building 217

Office Hours: MW 11:00am-11:50am in Weber 129

[Syllabus]

Tentative Schedule:

Week 1:

March 20: Course overview and introduction to topology, topological data analysis, and machine learning. [Slides]

March 22: Lab: python introduction and setup. [Jupyter Notebook]

Week 2:

March 27: Clustering, k-means clustering, hierarchical clustering, dendrograms. [Slides by Henry Adams and Lara Kassab]

March 29: Lab: clustering in python. [Jupyter Notebook], [Solutions]

Week 3:

April 3: Dimensionality reduction - PCA, multidimensional scaling.

April 5: Lab: dimensionality reduction in python. [Jupyter Notebook], [Solutions]

Week 4:

April 10: Data visualization - Reeb graphs and Mapper. [Slides]

April 12: Lab: Mapper in python. [Jupyter Notebook]

Week 5:

April 17: Persistent homology of point clouds, Vietoris-Rips complexes, the bottleneck and Wasserstein distances. [Slides]

April 19: Lab: persistence in python with Ripser. [Jupyter Notebook]

Week 6:

April 24: Persistence and machine learning - persistence landscapes and persistence images. [Slides]

April 26: Lab: landscapes and persistence images in python. [Jupyter Notebook], [Textures Example]

Week 7:

May 1: Persistence and machine learning - SVM, kNN, logistic regression. [Slides]

May 3: Lab: persistence and machine learning in python. [Jupyter Notebook]

Week 8:

May 8: Final presentations

May 10: Final presentations