Gaussian Kernel Width Generator for Support Vector Clustering

Clustering data into natural groupings has important applications in fields such as Bioinformatics. Support Vector Clustering (SVC) does not require prior knowledge of a dataset and it can identify irregularly shaped cluster boundaries. A major SVC challenge is the choice of an important parameter value, the width of a kernel function that determines a nonlinear transformation of the input data. Since evaluating the result of a clustering algorithm is a highly subjective process, a collection of different parameter values must typically be examined. However, no algorithm has been proposed to specify the parameter values. This paper presents a secant-like numerical algorithm that generates an increasing sequence of SVC kernel width values. An estimate of sequence length depends on spatial characteristics of the data but not the number of data points or the data’s dimensionality. The algorithm relies on a function that relates the kernel width value to the radius of the minimal sphere enclosing the images of data points in a high-dimensional feature space. Experimental results with 2D and higher-dimensional datasets suggest that the algorithm yields useful data clusterings.