Geometry in Mathematics of Data Science 2022
A Workshop at the Joint Math Meetings (JMM 2022), Virtual, April 6, 2022
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Whether it is clustering, classification, or regression, at a very basic level, many problems in data science can be reduced to understanding properties of collections of points living in a high-dimensional space. It's little wonder then that geometry has played an important (if sometimes understated) role in the field. Whether it is helping interpret and improve today's state-of-the-art models or driving progress toward the algorithms of tomorrow, geometry is a powerful lens with which to understand the principal algorithms and methods of data science. In this special session we will hear from some of the top researchers at the intersection of mathematics and data science, each of whom is using ideas or techniques from geometry (and topology) to push the field of data science forward.
8:00 AM
Fractal Analysis of the Urbanization Development in Boston: 2000-2020
Junze Yin, Boston University
8:30 AM
Topological and Geometric Methods in the Study of the Snow Surface Roughness
Rachel Neville1, Patrick Shipman2 and Steven Fassnacht2, (1)Northern Arizona University, (2)Colorado State University
9:00 AM
Framework for testing applicability of Takens’ theorem using persistent homology
Tegan Emerson, Pacific Northwest National Laboratory, Redmond, OR, Emilie Purvine, Pacific Northwest National Laboratory and Sarah Tymochko, Michigan State University, East Lansing, MI
9:30 AM
I Spy in the Sky: a Stable Topological Approach for Aerial Tracking Data
Sarah Tymochko, Michigan State University, Alexander Soloway, Pacific Northwest National Laboratory, Tim Doster, Pacific Northwest National Lab, Colin Olson, U.S. Naval Research Laboratory, Washington, DC and Tegan Emerson, Pacific Northwest National Laboratory, Redmond, OR
10:00 AM
10:30 AM
A Grassmannian Walk Through a Dataset: Improving Data Visualization with Geometry
Jordan Weaver, University of Washington and Henry Kvinge, Pacific Northwest National Laboratory, Seattle, WA
11:00 AM
Diffusion and Volume Maximization-Based Clustering of Highly Mixed Hyperspectral Images
Sam Polk, Tufts Univeristy and James M. Murphy, Tufts University, Medford, MA
11:30 AM
Wojciech Czaja, University of Maryland, College Park, MD, Ilya Kavalerov, Google and Weilin Li, Courant Institute, New York, NY
1:00 PM
Michael J Kirby, Colorado State University
2:00 PM
Local and Global Topological Complexity Measures of ReLU neural network functions
Julia Elisenda Grigsby1, Kathryn Anne Lindsey1 and Marissa Masden2, (1)Boston College, (2)University of Oregon
2:30 PM
Using the linear geometry of ReLU neural networks to detect out-of-distribution inputs
Grayson Jorgenson, Pacific Northwest National Laboratory, SEATTLE, WA and Henry Kvinge, Pacific Northwest National Laboratory, Seattle, WA
3:00 PM
Elizabeth O'Reilly, Caltech, Pasadena, CA
3:30 PM
Nicolas Courts, University of Washington; Pacific Northwest National Laboratory and Henry Kvinge, Pacific Northwest National Laboratory, Seattle, WA
4:00 PM
Linearizing data science problems using transport and other Lagrangian embeddings
Gustavo Rohde, University of Virginia, Charlottesville, VA
4:30 PM
Word2Sphere: Toward geometrically interpretable language models
Julien Chaput, UTEP/PNNL, El Paso, TX
5:00 PM
Lara Kassab1, Henry Adams2 and Mark Blumstein2, (1)Colorado State University, Seattle, WA, (2)Colorado State University
5:30 PM
Scott Mahan, University of California, San Diego
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