Title: Fast Incremental SVDD Learning Algorithm with the Gaussian Kernel,
Abstract: Support vector data description (SVDD) is a machine learning technique that
is used for single-class classification and outlier detection. The idea of SVDD
is to find a set of support vectors that defines a boundary around data. When
dealing with online or large data, existing batch SVDD methods have to be rerun
in each iteration. We propose an incremental learning algorithm for SVDD that
uses the Gaussian kernel. This algorithm builds on the observation that all
support vectors on the boundary have the same distance to the center of sphere
in a higher-dimensional feature space as mapped by the Gaussian kernel
function. Each iteration involves only the existing support vectors and the new
data point. Moreover, the algorithm is based solely on matrix manipulations;
the support vectors and their corresponding Lagrange multiplier $\alpha_i$'s
are automatically selected and determined in each iteration. It can be seen
that the complexity of our algorithm in each iteration is only $O(k^2)$, where
$k$ is the number of support vectors. Experimental results on some real data
sets indicate that FISVDD demonstrates significant gains in efficiency with
almost no loss in either outlier detection accuracy or objective function
value.