Support Vector Clustering with RBF Gaussian Kernel Parameter Optimization

Abstract

Grouping the data according to their mutual
similarities is called clustering which is an unsupervised
technique. We have introduced an improved version of
Support Vector Clustering (SVC) technique with automatic
parameter tuning in this paper. Using Gaussian RBF kernel,
the data points are mapped into a higher dimensional feature
space. The objective function becomes to find the minimal
enclosing sphere for all data points in the kernel space. This
sphere, when mapped back to the data space, separates into
several components with irregular boundaries, enclosing
separate clusters of points. There are two tuning parameters in
SVC, soft margin penalty constant and width of the Gaussian
kernel which are varied and used to attain smooth cluster
boundaries. It is difficult to accurately select both of these
parameters manually using k-fold Cross Validation. So, we
have employed an optimization technique to find out RBF
sigma parameter tuning which was originally proposed by
Cheng Hsuan Li et.al for Support Vector Machines (SVM).
The optimal kernel RBF sigma value for SVC is calculated
which is more accurate and computationally efficient and
accurate compared to k-fold cross validation method. We have
performed experiments on artificial and public datasets from
UCI public repository. Promising outcome results show that
this technique is effective in kernel parameter optimization for
cluster analysis.

Keywords - Support Vector Machine, RBF kernel, cross
validation, unsupervised learning