Engineering multilevel support vector machines

The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced class sizes. Typically, nonlinear kernels produce significantly higher classification quality to linear kernels but introduce extra kernel and model parameters. Thus, the parameter fitting is required to increase the quality but it reduces the performance dramatically. We introduce a generalized fast multilevel framework for SVM and discuss several versions of its algorithmic components that lead to a good trade-off between quality and time. Our framework is implemented using PETSc which allows integration with scientific computing tasks. The experimental results demonstrate significant speed up compared to the state-of-the-art SVM libraries.