### Roger Fletcher FRS (University of Dundee and University of Edinburgh)

#### Separating clusters of points and training SVMs

*Joint work with Gaetano Zanghirati.*

*Tuesday 13 November 2007 at 16.00, JCMB 5327*

##### Abstract

Finding the hyperplane that best separates two clusters of points is an
important problem in many areas, and particularly in training Support Vector
Machines (SVMs). The desirable solution is shown to satisfy an NLP problem
with a single nonlinear constraint. Existing methodology transforms this
problem to a dual convex QP problem, but is shown to be unreliable in many
situations.

A new proposal based on the SQP method is described, along with numerical
experience. Potential applications can have a very large number of points in
the clusters and are computationally challanging. We outline an approximation
scheme based on low-rank Cholesky factors.

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