CMAI Colloquium w/ Prof. Mark Embree

Date:

Friday March 11, 2022 at 10:00 am (Eastern Time) 

Speaker:

Prof. Mark Embree
Virginia Tech

Title:

CUR Matrix Factorizations: Algorithms, Analysis, Applications

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Abstract:

Interpolatory matrix factorizations provide alternatives to the singular value decomposition (SVD) for obtaining low-rank approximations; this class includes the CUR factorization, where the C and R matrices are subsets of columns and rows of the target matrix. While interpolatory approximations lack the SVD's optimality, their ingredients are easier to interpret than singular vectors: since they are copied from the matrix itself, they inherit the data's key properties (e.g., nonnegative/integer values, sparsity, etc.). We shall provide an overview of these approximate factorizations, show how they can be analyzed using interpolatory projectors, and describe a method for their construction based on the Discrete Empirical Interpolation Method (DEIM). We will then describe use of this factorization for two applications: footstep analysis from building vibrations, and identification of representative survey responses from a text collection.

This talk describes joint work with Dan Sorensen, Pablo Tarazaga, Ed Gitre, and students.