CS 6170 : Computational Topology

January 01, 2017

School of Computing, University of Utah, Salt Lake City, Utah
Link to the course page  

The objective of this class was to enable the students to become familiar with methods in Topological Data Analysis (TDA), from theory, algorithms and applications perspectives. TDA is an emerging area in exploratory data analysis and data mining. 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 audience for the class included graduate students and highly motivated upper level undergraduate students. There were no formal prerequisites for this class beyond basic knowledge of data structures and algorithmic techniques. Particularly, students were not required to be majoring in Computer Science. The course covered the following topics:

• Basic concepts (point clouds, graphs, topological spaces, manifolds).
• 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).