DATE: | Thursday, December 4th |

TIME: | 11:00 AM - 12:00 PM |

PLACE: | McConnell 103 |

TITLE: | Separation made easier |

SPEAKER: | David Bremner, Computer Science, University of New Brunswick |

Whether two sets are separable by hyperplanes is invariant under affine
transformations, while
distance is not. The near universal reduction of separation problems in practice to distance
computations is on the surface thus a bit of a mystery. In this talk I will argue that the
connection between distance and separation is necessary and natural as soon as one asks for the
``best'' separating hyperplane. On the other hand, it is often much more convenient to work with
distance metrics different from the standard Euclidean one. It turns out that for polytopal
metrics a strong duality relationship between distance and separation allows the straightforward
computation of optimal separating hyperplanes by solving a primal-dual pair of linear programs. An
especially interesting feature of this framework is that it works for input given explicitly as
sets of points (where an LP solution is relatively well known, even for the Euclidean metric), but
also for input given implicitly as intersections of halfspaces and Minkowski sums of line
segments. I will round out the talk by discussing some possible approaches to the case when two
sets are not separable by a hyperplane, and some connections with problems in pattern
classification.

(Work with Thomas Burger and Peter Gritzmann)

Direct questions, comments, additions to and removals from the mailing list, and suggestions for speakers to us at beezer at cs.mcgill.ca.

Web Address: www.cs.mcgill.ca/~beezer/Seminars/seminar99.html