Geometry in Mathematics of Data Science 2021

A Workshop at the Joint Math Meetings (JMM 2021), Virtual, January 6, 2021

Much of the data that is fueling the current rapid advances in data science and machine learning is very high dimensional. This poses challenges both in terms of building algorithms that can capture meaningful structure and also building analytical techniques that help to understand what that structure means. Mathematicians working in geometry have more than a hundred years worth of finely-developed machinery whose purpose is to give structure to, help build intuition about, and generally better understand the spaces beyond those that we can easily visualize. This special session will focus on work which shows how methods from geometry are currently being used to answer challenging questions in data science and helping to pose new questions in mathematics in the process. These range from the use of well-known geometric spaces such as Grassmann and flag manifolds as a framework to analyze data, to the use of Lie theory in computer vision, to new questions in metric geometry inspired by data science problems.

Organizers:

Henry Kvinge, Pacific Northwest National Laboratory
Tegan Emerson, Pacific Northwest National Laboratory
Carlos Ortiz Marrero, Pacific Northwest National Laboratory
Tim Doster, Pacific Northwest National Laboratory

8:00 a.m.
Non-congruent curves with identical signatures.
Eric Geiger*, North Carolina State University
Irina A. Kogan, North Carolina State University
(1163-51-1471)
8:30 a.m.
Riemannian Frank-Wolfe Methods and Applications.
Melanie Weber*, Princeton University
Suvrit Sra, Massachusetts Institute of Technology
(1163-49-111)
9:00 a.m.
Improved sufficient conditions for identifiable nonnegative matrix factorization.
Tim Marrinan*, Université de Mons
(1163-15-510)
9:30 a.m.
The critical locus of the loss function of deep neural networks.
Yaim Cooper*, US
(1163-51-1237)
10:00 a.m.
Statistical Analysis of Shapes and Shape Deformations in 3D.
Hossein Dabirian, Department of Mathematics, University of Houston
Jiwen He, Department of Mathematics, University of Houston
Robert Azencott, Department of Mathematics, University of Houston
Andreas Mang*, Department of Mathematics, University of Houston
(1163-49-38)
10:30 a.m.
The Geometry of Deep Networks: Power Diagram Subdivision.
Randall Balestriero*, Rice University
Romain Cosentino, Rice University
Behnaam Aazhang, Rice University
Richard G Baraniuk, Rice University
(1163-52-1325

2:15 p.m.
A Performance Guarantee for Spectral Clustering.
Shaofeng Deng*, UC Davis
March Boedihardjo, UCLA
Thomas Strohmer, UC Davis
(1163-49-466)
2:45 p.m.
A Geometric Measure Theory Approach to Identify Complex Structural Features on Soft Matter Surfaces.
Enrique Alvarado*, Washington State University
Zhu Liu, Washington State University
Michael J Servis, Argonne National Laboratory
Bala Krishnamoorthy, Washington State University
Aurora E Clark, Washington State University
(1163-53-1284)
3:15 p.m.
Fast Pairwise Optimal Transport and Linear Classification for Nonlinear Problems.
Alexander Cloninger*, University of California San Diego
Caroline Moosmueller, University of California San Diego
(1163-65-515)
3:45 p.m.
MaxFun Pooling - maximal function-inspired pooling operation.
Wojciech Czaja*, University of Maryland
Weilin Li, Courant Institute
Yiran Li, Target Corporation
Mike Pekala, Independent Scientist
(1163-42-1634)
4:15 p.m.
Reactive sensing and multiplicative frame super-resolution.
John J. Benedetto*, Norbert Wiener Center, Department of Mathematics, U. of Maryland, College Park
Michael R. Dellomo, Norbert Wiener Center, Department of Mathematics, U. of Maryland, College Park
(1163-42-245)
4:45 p.m.
Applied topology: From global to local.
Henry Adams*, Colorado State University
(1163-55-150)
5:15 p.m.
Flag Manifolds in Data Analysis.
Michael Kirby, Colorado State University
Xiaofeng Ma, Colorado State University
Chris Peterson*, Colorado State University
(1163-51-388)
5:45 p.m.
Encoding intrinsic variation in data: a survey of the use of Grassmann, flag, and Stiefel manifolds in data science.
Elin Farnell*, Amazon
(1163-51-965)

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