Department of Mathematics

Geometry and Topology

  •  Projective coordinates for the analysis of data
  •  01/12/2017
  •  2:00 PM - 2:50 PM
  •  C304 Wells Hall
  •  Jose Perea, MSU

Barcodes - the persistent homology of data - have been shown to be effective quantifiers of multi-scale structure in finite metric spaces. Moreover, the universal coefficient theorem implies that (for a fixed field of coefficients) the barcodes obtained with persistent homology are identical to those obtained with persistent cohomology. Persistent cohomology, on the other hand, is better behaved computationally and allows one to use convenient interpretations such as the Brown representability theorem. We will show in this talk how one can use persistent cohomology to produce maps from data to (real and complex) projective space, and conversely, how to use these projective coordinates to interpret persistent cohomology computations.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science