Kernel bandwidth selection for SVDD: The sampling peak criterion method for large data

Support vector data description (SVDD) provides a useful approach, with various practical applications, for constructing a description of multivariate data for single-class classification and outlier detection. The Gaussian kernel that is used in SVDD formulation allows a flexible data description defined by observations that are designated as support vectors. The data boundary of such a description is nonspherical and conforms to the geometric features of the data. By varying the Gaussian kernel bandwidth parameter, the SVDD-generated boundary can be made either smoother (more spherical, which might lead to underfitting), or tighter and more jagged (which might result in overfitting). Kakde et al. [1] proposed a peak criterion for selecting an optimal value of the kernel bandwidth to strike a balance between the data boundary smoothness and a method's ability to capture the general geometric shape of the data. The peak criterion approach involves training the SVDD at various values of the kernel bandwidth parameter. When training data sets are large, the time required to obtain the optimal value of the Gaussian kernel bandwidth parameter according to the peak method can become prohibitively large. This paper proposes an extension of the peak method for the case of large data. The proposed method produces good results when applied to several data sets. Two existing alternative methods of computing the Gaussian kernel bandwidth parameter (coefficient of variation and distance to the farthest neighbor) were modified in order to allow comparison with the proposed method on convergence. Empirical comparison demonstrates the advantage of the proposed method.