Applied Topology and Data Analysis Fall 2016

Course Description: In recent years it has became clear that studying the topological features of data gives important insights on data analysis and understanding. The topology of data reveals the underlying structure of the data and gives a summary and interpretation for that data. This course introduces the theoretical foundations and basics of this new emerging field and teaches the students some of the practical algorithms in topological data analysis.

Target Audience: This course is suitable for upper undergraduate students and graduate students in computer science, mathematics, physics, mechanical and electrical engineering, or other related fields. This course is ideal for students who have interests in data sciences, data visualization, signal processing, machine learning, as well as for students who are interested in the computational aspects of topology and their applications.

Goals:  Learn the fundamental concepts and the mathematical foundation of topology that is useful for computing with data.  Development of algorithmic tools implementing topological concepts for use in sciences and engineering.  Understand some of the practical algorithms in topological data analysis and learn how to deal with real data.

Course Topics : Topics include, but are not limited to:

  •  Basics Topology 
  • Complexes on Data
  • Basic of Homology 
  • Persistence Homology 
  • PL Morse-Theory 
  • Topological Techniques in Data Visualization 
  • Reeb Graph from Data

Prerequisites: A semester of programing experience is expected and basics of linear algebra. No prior knowledge of topology is required.

References : 

  • A Short Course in Computational Geometry and Topology, Herbert Edelsbrunner.
  • Computational topology, Herbert Edelsbrunner and John L. Harer, AMS 
  • Topology for Computing, Afra J. Zomorodian. 
  • Curve and surface reconstruction: Algorithms with mathematical analysis, Tamal K. Dey, Cambridge U. Press 

Additional references from research papers will be announced later in class.