  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 which requires computationally expensive fitting. This
increases the quality but also reduces the performance dramatically. We
introduce a generalized fast multilevel framework for regular and weighted 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 an easy integration with scientific computing tasks. The
experimental results demonstrate significant speed up compared to the
state-of-the-art nonlinear SVM libraries.
  Reproducibility: our source code, documentation and parameters are available
at https:// github.com/esadr/mlsvm.
