The links below include both recommended as well as
supplementary reading
for those who wish to go deeper into a subject. Recommended vs
supplementary reading will be distinguished at a later date.
| Week 1 | Topological Data Analysis: Software Mapper |
| Aug 26 video, pptx, pdf
| Extracting
insights from the shape of complex data using topology
P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M.
Vejdemo-Johansson, M. Alagappan, J. Carlsson, G. Carlsson
(2013)
|
| Aug 28 video, pptx, pdf
| Topology based
data analysis identifies a subgroup of breast cancers with a unique
mutational profile and excellent survival
M. Nicolau, A. J. Levine, G. Carlsson (2011)
|
| Aug 30 video, pptx, pdf
|
Download Mapper
for Matlab
Python Mapper
Graphviz
Web tool: Progression
Analysis of Disease - PAD (includes Mapper)
Ayasdi Iris,
academic trial
|
|
Additional readings:
Topological Methods for the Analysis of High Dimensional
Data Sets and 3D Object Recognition
G. Singh , F. Memoli, G. Carlsson (2007)
Topology
and data, G Carlsson (2009) (Mapper: p. 281 - 289)
DNA
MICROARRAY VIRTUAL LAB,
youtube
video
How to Analyze DNA Microarray Data,
Howard Hughes Medical Institute
Pearson
Product-Moment Correlation
|
| Week 2 |
Homology |
Sept 2 | Holiday: No class |
| Sept 4
video,
pptx, pdf |
Section 2 in H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and
simpliction, Discrete and Computational Geometry 28, 2002, 511-533.
Discriminative
persistent homology of brain networks, Hyekyoung Lee; Chung, M.K.; Hyejin Kang; Bung-Nyun Kim; Dong Soo Lee, Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on , vol., no., pp.841,844, March 30 2011-April 2 2011.
|
| Sept 6
video, pptx, pdf
|
A. Zomorodian and G. Carlsson , Computing persistent homology, Discrete and Computational Geometry, 33 (2), pp. 247-274. Jan 2005
4.1 - 4.3 in Herbert Edelsbrunner and John L. Harer, Computational Topology,
American Mathematical Society (December 8, 2009)
google books
preview
Ch 4 and sect 7.3.1 in
Afra J. Zomorodian, Topology for Computing (Cambridge Monographs on
Applied and Computational Mathematics), Cambridge University Press
(September 28, 2009) google books preview
|
| Additional readings (for Sept 4)
Persistent
Brain Network Homology From the Perspective of Dendrogram, Hyekyoung Lee; Hyejin Kang; Chung, M.K.; Bung-Nyun Kim; Dong Soo Lee, Medical Imaging, IEEE Transactions on , vol.31, no.12, pp.2267,2277, Dec. 2012.
|
| Week 3 |
|
| Sept 9
video,
pptx, pdf
| Create your own homology
Ghrist's A Sequence of Homologies
video
(pdf). From IMA New Directions Short Course
Applied Algebraic Topology
June 15-26, 2009
|
| Sept 11
video,
pptx, pdf
| Persistent homology
Topology
and data, G Carlsson (2009)
H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and
simpliction, Discrete and Computational Geometry 28, 2002, 511-533.
Ch 7 in
Afra J. Zomorodian, Topology for Computing (Cambridge Monographs on
Applied and Computational Mathematics), Cambridge University Press
(September 28, 2009) google books preview
|
| Sept 13
video,
pptx, pdf
|
Persistance homology (cont.)
|
| Additional readings
Klein bottle
Topological analysis of population activity in visual cortex,
Gurjeet Singh,
Facundo Memoli,
Tigran Ishkhanov,
Guillermo Sapiro,
Gunnar Carlsson,
Dario L. Ringach, J Vis. 2008 Jun 30;8(8):11.1-18
Persistent
Homology — a Survey. Herbert Edelsbrunner
and John Harer, Contemporary Mathematics 453 (2008), 257 - 282
|
| Week 4 |
|
| Sept 16
video,
pptx, pdf
|
Persistent homology III
Javaplex,
Javaplex tutorial
|
| Sept 18
video,
pptx, pdf
|
NKI
data,
Array5yr.csv
|
| Sept 20
,
pptx, pdf
| Persistent homology IV |
| Additional readings
Mathworks Matlab Tutorials
Kaggle data analysis competitions
Data for MATLAB hackers (pre-2010)
http://yann.lecun.com/exdb/mnist/
Using the MNIST Dataset
|
| Week 5 |
|
| Sept 23 | |
| Sept 25 | |
| Sept 27 | |
| Additional readings |
| Week 6 |
|
| Sept 30 | |
| Oct 2-4 |
IMA pre-workshop (Oct 2-4):
An
Introduction to
Statistics and Probability for Topologists |
| Additional readings |
| Week 7 |
| Oct 7 - 11 |
IMA workshop: Topological Data
Analysis
|
| Week 8 |
Cohomology |
| Oct 14 | |
| Oct 16 | |
| Oct 18 | |
| Additional readings |
| Week 9 |
Cohomology |
| Oct 21 | |
| Oct 23 | |
| Oct 25 | |
| Additional readings |
| Week 10 |
| Oct 28 - Nov 1 |
IMA workshop: Modern Applications
of Homology and Cohomology |
| Week 11 |
|
| Nov 4 | |
| Nov 6 | |
| Nov 8 | |
| Additional readings |
| Week 12 |
|
| Nov 11 | |
| Nov 13 | |
| Nov 15 | |
| Additional readings |
| Week 13 |
|
| Nov 18 | |
| Nov 20 | |
| Nov 22 | |
| Additional readings |
| Nov 25 - 29 |
Thanksgiving break |
| Week 14 |
|
| Dec 2 | |
| Dec 4 | |
| Dec 6 | |
| Additional readings |
| Week 15 |
| Dec 9-13 |
IMA workshop: Topological
Structures in Computational Biology
|
Spring Activities: While the official course will end in December, we can
continue online seminars/discussion meetings.