# Scaling up support vector data description by using core-sets

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Calvin S. Chu, Ivor W. Tsang, James T. Kwok

**Abstract:**
Support vector data description (SVDD) is a powerful kernel method that has
been commonly used for novelty detection. While its quadratic programming
formulation has the important computational advantage of avoiding the problem
of local minimum, this has a runtime complexity of $O(N^3)$, where $N$ is the
number of training patterns. It thus becomes prohibitive when the data set is
large. Inspired from the use of core-sets in approximating the minimum
enclosing ball problem in computational geometry, we propose in this paper an
approximation method that allows SVDD to scale better to larger data sets.
Most importantly, the proposed method has a running time that is only linear
in $N$. Experimental results on two large real-world data sets demonstrate
that the proposed method can handle data sets that are much larger than those
that can be handled by standard SVDD packages, while its approximate solution
still attains equally good, or sometimes even better, novelty detection
performance.
*Proceedings of the International Joint Conference on Neural Networks
(IJCNN 2004)*, pp.425-430, Budapest, Hungary, July 2004.

Pdf:
http://www.cs.ust.hk/~jamesk/papers/ijcnn04.pdf

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