DIFFERENTIAL GEOMETRY/PDE/NUMERICAL ANALYSIS SEMINAR

                              Monday, March 4

                              Padelford C401
                                  3:45 pm

                           Jose Martinez-Morales
                        (University of Washington)


             Extremal Properties of Principal Manifolds in R^n


Principal manifolds generalize the concept of principal curves, which were
introduced to formalize the notion of "a curve passing through the middle
of a dataset."  Vaguely speaking, a manifold is said to pass through the
middle of a dataset if every point on the manifold is the average of the
observations projecting onto it.  This idea can be made precise by defining
principal manifolds for probability densities.  In this talk we study
principal manifolds in R^n.  Principal manifolds are critical points of the
expected squared distance from the data. However, all principal manifolds
are saddlepoints.  We seek a condition to break this saddlepointness.


For more information about this seminar, view the Differential Geometry
Seminar World-Wide Web page at

    https://www.math.washington.edu/~lee/Seminars/dg.html


To request disability accommodations, contact the Office of the ADA
Coordinator, at least ten days in advance of the event: 543-6450 (voice);
543-6452 (TDD); 685-3885 (FAX); access@u.washington.edu (E-mail).