Support vector data description (SVDD) is a machine learning technique thatis used for single-class classification and outlier detection. The idea of SVDDis to find a set of support vectors that defines a boundary around data. Whendealing with online or large data, existing batch SVDD methods have to be rerunin each iteration. We propose an incremental learning algorithm for SVDD thatuses the Gaussian kernel. This algorithm builds on the observation that allsupport vectors on the boundary have the same distance to the center of spherein a higher-dimensional feature space as mapped by the Gaussian kernelfunction. Each iteration only involves the existing support vectors and the newdata point. The algorithm is based solely on matrix manipulations; the supportvectors and their corresponding Lagrange multiplier $lpha_i$'s areautomatically selected and determined in each iteration. It can be seen thatthe complexity of our algorithm in each iteration is only $O(k^2)$, where $k$is the number of support vectors. Our experimental results on some real datasets show that our incremental algorithm achieves similar F-1 scores with muchless running time.
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