Geometric Data Analysis Reading Group

** Go to the new Geometric Data Analysis Reading Group site **

Add yourself to the mailing list http://mailman12.u.washington.edu/mailman/listinfo/geometry

We will read and discuss foundational papers and themes of Geometric Data Analysis such as

what is Topological Data analysis

manifold learning algorithms

dimension estimation

the Laplacian: what it tells us about the data, how to estimate it

More information and a web page to come soon. If you are interested in participating, please email the organizers. We will aim to meet approximately every other week, i.e. to have 4-5 meetings this quarter.

For student participants: You will not be required to make a presentation/lead a discussion of a paper this quarter, but if you plan to volunteer for one, you can sign up for 1 stat 600 credit with one of the organizers.

List of suggested papers for Spring 2019

Spectral clustering. Start with this tutorial some variations based on local PCA and this , path based and this one, with more meat but harder to read The tutorial(s) would take 1 session, with the extras another session. There are zillions more papers, and I could recommend also this short paper on Self-tuning spectral clustering FYI.
I also thought based on previous meetings that 1/2 meeting on comparing clusterings would be useful. I will add a tutorial and a few more refs shortly.
Copula PCA

Schedule for Spring 2019

[4/10] Sam Koelle on the manifold of shapes. A book and a seminal statistics paper by Le and Kendall

[4/24] Hanyu Zhang Diffusion maps https://www.sciencedirect.com/science/article/pii/S1063520306000546 and https://arxiv.org/abs/0811.0121

[5/8] Zhenman Yuan Spectral clustering

[5/29] Sam Koelle General Exam 1:30 PM PDL C301

[6/5] Daniel Ting -- tentative

Schedule for Winter 2019

[1/30] Gang Cheng on How to tell when a clustering is approximately correct...

[2/6] Yen-Chi Chen Statistical inference with local optima

[2/20] Malcolm Wolff and Hanyu Zhang Kernel density estimation with Locality Sensitive Hashing (Part II)

[3/6] Yikun Zhang 2 step EM for Gaussian mixtures http://cseweb.ucsd.edu/~dasgupta/papers/em.pdf

Schedule for Winter 2018

[1/11] Sam Koelle will present Metric manifold learning: preserving the intrinsic geometry (slides)

[1/25] Yu-Chia Chen will present Improved Graph Laplacian via geometric self-consistency

[2/1]

[2/22]

[3/1]

Schedule for Autumn 2017

[11//30] Daniel Ting (Tableau) on understaning Laplacians (tentative title!)

[11/16] Kitty Mohammed Manifold Learning with KDE and Local PCA

based on this recent paper and this older paper

Werner shared this paper Approaches to analysis of data that concentrate near higher-dimensional manifolds by Jerome H. Friedman, John W. Tukey and Paul A. Tukey

paper on Estimating the reach of a manifold (thanks to Yen-chi)

[11/2] Sheridan Grant The nuts and bolts of persistent homology

after this seminal paper

to use during and before the meeting PHdemo.m and 145Notes2015.pdf

[10/19] Marina Meila Algorithmics of Manifold Learning

Skim through these before the meeting

light intro to manifold learning

from here have a look at Metric Scaling (by Werner Stuetzle) and Intro to non-parametric density estimation (only the light parts) (annotated by Werner)

Other resources

Slightly more technical tutorial on dimension reduction by Ali Ghodsi

Less technical, other aspects, Marina's slides on manifold learning

Principal Curves and Surfaces paper by Ozertem and Erdogmus

[10/5] Yen-chi Chen Introduction to TDA after this paper