Fast Support Vector Machine classification of very large datasets

In many classification applications, Support Vector Machines (SVMs) have proven to be highly performing and easy to handle classifiers with very good generalization abilities. However, one drawback of the SVM is its rather high classification complexity which scales linearly with the number of Support Vectors (SVs). This is due to the fact that for the classification of one sample, the kernel function has to be evaluated for all SVs. To speed up classification, different approaches have been published, most which of try to reduce the number of SVs. In our work, which is especially suitable for very large datasets, we follow a different approach: as we showed in (Zapien et al. 2006), it is effectively possible to approximate large SVM problems by decomposing the original problem into linear subproblems, where each subproblem can be evaluated in Omega(1). This approach is especially successful, when the assumption holds that a large classification problem can be split into mainly easy and only a few hard subproblems. On standard benchmark datasets, this approach achieved great speedups while suffering only sightly in terms of classification accuracy and generalization ability. In this contribution, we extend the methods introduced in (Zapien et al. 2006) using not only linear, but also non-linear subproblems for the decomposition of the original problem which further increases the classification performance with only a little loss in terms of speed. An implementation of our method is available in (Ronneberger and et al.) Due to page limitations, we had to move some of theoretic details (e.g. proofs) and extensive experimental results to a technical report (Zapien et al. 2007).