CS 6170: Computational Topology

Topological Data Analysis: The New Frontier of Data Science

Spring 2017

Scribe Information

Scribe Template: Each student is required to scribe for at least one lecture. The scribe LaTex template can be found here.

If you are unfamiliar with LaTex, please study from an online tutorial (for example, at www.latex-tutorial.com), or contact the TA for a short introduction.

Final Project Presentations

Please contact the TA to sign up as soon as possible.

Schedule (subject to change, guest lectures marked with a *)

Book chapters
Handouts and Comments
1 1/10 Introduction Special Topics Lecture 01
1/12 Basics: graphs, connected components A.I Lecture 02 Scribe 02
Tim Sodergren
2 1/17 Basics: topological spaces, union-find A.II Lecture 03 Scribe 03
Jessica Lohse
1/19 Complexes on data;
Application: sensor networks
A.III Lecture 04 [Quiz 1] [Quiz 1 Solution] Scribe 04
Jadon Wagstaff
3 1/24 Simplicial Complexes A.III Lecture 05 Scribe 05
Prem Narayanan
1/26 Vietoris-Rips, Cech, Delaunay and Alpha Complexes B.IV Lecture 06 Scribe 06
Sam Leventhal
4 1/31 Homotopy equivalence, manifold A.II Lecture 07 Scribe 07
Avani Sharma and Navid Farhoudi
2/2 Homology B.IV Lecture 08 Scribe 08
Celeste Hollenbeck
5 2/7 Persistent homology in a nutshell;
Application: TDA for brain networks*
Special Topics Lecture 09 [Youtube: Introduction to Persistent Homology By Matthew Wright] [Persistent Homology of Complex Networks] [Kernel Partial Least Squares Regression for Relating Functional Brain Network Topology to Clinical Measures of Behavior] Scribe 09
Vipin Jose
2/9 Cohomology in a nutshell, dimension reduction with circular coordinates; Application: memory reference frame analysis* Special Topics Lecture 10 [Topological Analysis and Visualization of Cyclical Behavior in Memory Reference Traces ] [Branching and Circular Features in High Dimensional Data] [Persistent Cohomology and Circular Coordinates] Scribe 10
Adam Conkey
6 2/14 Computing persistent homology C.VII Lecture 11 Scribe 11
Kevin Childers
2/16 Computing homology B.IV Lecture 12 Scribe 12
Waiming Tai
7 2/21 Computing homology and persistent homology, revisited Lecture 13 Scribe 13
Sahar Mehrpour
2/23 Duality between homology and cohomology B.V Lecture 14 [Quiz 2] [Quiz 2 Solution] Scribe 14
Drew McClelland
8 2/28 Persistent homology for large data: software packages* Special Topics Lecture 15 [Miniproject 1 (Due Mar 21)]
[Project Description] [Datasets]
Scribe 15
Paul English
3/2 Persistent homology for large data: spectral sequence, clear and compress* Special Topics Lecture 16 [Persistent Homology Computation with a Twist] [Clear and Compress: Computing Persistent Homology in Chunks] [Distributed Computation of Persistent Homology] Scribe 16
Zahra Fahimfar
9 3/7 Morse function B.VI Lecture 17 Scribe 17
Yiliang Shi and Benwei Shi
3/9 Morse lemma and Reeb graph B.VI Lecture 18 Scribe 18
Mohammed Musaddiq and Justin Boyer
10 3/14 Happy Spring Break! Start thinking about final project no later than this date!
3/16 Happy Spring Break!
11 3/21 Piecewise linear function and computing Reeb graph B.VI Lecture 19 Scribe 19
Adam Brown
3/23 Multivariate data analysis: mapper Special Topics Lecture 20 [Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition] [Extracting Insights from the Shape of Complex Data Using Topology] [Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival] Scribe 20
Gurupragaash Annasamymani
12 3/28 More on mapper Special Topics Lecture 21 [Final Project Proposal Due]
Start final project no later than this date!
Scribe 21
Zhimin Li
3/30 Stability of persistence diagrams C.IX
Special Topics
Lecture 22 [Stability of Persistence Diagrams] Scribe 22
Ramkashyap Seethamraju
13 4/4 Elevation for protein docking Special Topics Lecture 23 [Extreme Elevation on a 2-Manifold] [Coarse and Reliable Geometric Alignment for Protein Docking] [Computing Elevation Maxima by Searching the Gauss Sphere ] Scribe 23
Will Usher
4/6 More on Elevation function; Reeb space Special Topics Lecture 24 [Quiz 3] [Quiz 3 Solution] [Elevation in a nutshell] Scribe 24
Di Wang
14 4/11 Data Science for Topologists Special Topics Lecture 25 [Data Science for Topologists: By Jennifer Gamble] [Topological Complexity in Protein Structure: By Erica Flapan] Talks at AWM Research Symposium WinCompTop Special Session: Applications of Topology and Geometry April 8-9, 2017 Scribe 25
Qi Wu
4/13 TDA for vector field data Special Topics Lecture 26 [Robustness for VF Simplification] Scribe 26
Michael Matheny
15 4/18 Persistent local homology and its applications Special Topics Lecture 27 [Local Homology Transfer and Stratification Learning] Scribe 27
Pavol Klacansky
4/20 Persistent local homology and its applications Special Topics Lecture 28 [Exploring Persistent Local Homology in Topological Data Analysis] Scribe 28
Matthew Territo
16 4/25 Morse-Smale Complexes
Scalable TDA via sparsification*
Special Topics Lecture 29 [Quiz 4] [ Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds ] [Lecture notes by Guoning Chen] [MSC in nutshell] [A Geometric Perspective on Sparse Filtrations] Scribe 29
Sheyne Anderson and Dietrich Geisler
17 5/1 Final Project Presentation Day 1 1:00 p.m. - 5:30 p.m. WEB 3840
5/2 Final Project Presentation Day 2 1:00 p.m. - 5:30 p.m. WEB 3840
5/3 Final Project Due 11:59 p.m.
(Report and Source Code)


TDA Classes on the Web:

CPS296.1: Computational Topology By Herbert Edelsbrunner @ Duke
CSE 5339: Computational Topology and Data Analysis By Tamal K Dey @ OSU
CS 598: Computational Topology By Jeff Erickson @ UIUC
CS 468: Introduction to Computational Topology By Afra Zomorodian @Stanford
CSCI 491/591: Computational (Geometry and) Topology By Brittany Terese Fasy @ MSU

Other TDA Resources on the Web:


Topology Classes/Books on the Web:

Topology Illustrated by Peter Saveliev @ Marshall