**Local
SVM classification based on Triangulation**

**Glenn
Fung**

In recent years Support Vector Machines
(SVM) have been used widely for classification, regression and in general,
supervised and unsupervised learning.

In this work I will concentrate on two-class
classification. Briefly described, a support vector machine defines a
hyperplane that classifies points by assigning them to one of two disjoint
halfspaces. In the case when the set is not linearly separable, the points
are mapped to a higher dimensional
space by using a nonlinear kernel. In this new high dimensional space, a linear
classifier is appropriate. Two known difficulties that confront large data
classification by a nonlinear kernel are:

1-
The possible dependence of the nonlinear separating
surface on the entire dataset, which creates unwieldy storage and computational
problems that prevent the use of nonlinear kernels for anything but a small
dataset.

2- The sheer size of the mathematical
programming problem that needs to be solved.

I am proposing a new method to classify
points on the plane that addresses the two points mentioned above. In order to
achieve this, the dataset has to be divided in different smaller zones (using
Delaunay triangulation) where the problem to solve is smaller and thus easier
to solve. Once the dataset is divided, each subset is treated as an independent
subset where a SVM is applied to find a nonlinear separating surface that is
based in a much smaller dataset.

The complete report can be found here:

http://www.cs.wisc.edu/~gfung/cs558proj.ps

PowerPoint presentation:

http://www.cs.wisc.edu/~gfung/talks/cs558projtt.ppt