CUR Matrix Factorizations: Algorithms, Analysis, Applications

2 June 2016
14:00
Professor Mark Embree
Abstract
Interpolatory matrix factorizations provide alternatives to the singular value decomposition 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, describe how they can be analyzed using interpolatory projectors, and introduce a new method for their construction based on the
Discrete Empirical Interpolation Method (DEIM).  To conclude, we will use this algorithm to gain insight into accelerometer data from an instrumented building.  (This talk describes joint work with Dan Sorensen (Rice) and collaborators in Virginia Tech's Smart Infrastucture Lab.)
  • Computational Mathematics and Applications Seminar