[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Paul Brooks (Virginia Commonwealth University)
November 13, 2015
2pm - 3pm
Abstract: Hospital-level antibiotic resistance data and human microbiome data serve as a motivation for developing robust methods for PCA. We present two methods for PCA based on minimizing the L1 distance of points to fitted (1) hyperplanes and (2) lines. Both problems are naturally written as nonlinear nonconvex optimization problems. Surprisingly, the L1-norm best-fit hyperplane can be found by solving a small number of linear programs. Finding the L1-norm best-fit line was recently shown to be NP-Hard (Gillis and Vavasis, 2015). Analysis of relevant linear programming formulations reveals properties of L1 projection on a line. These properties suggest a method for estimating the best-fit line that can also be used for variable selection.