  The support vector machines (SVM) is one of the most widely used and
practical optimization based classification models in machine learning because
of its interpretability and flexibility to produce high quality results.
However, the big data imposes a certain difficulty to the most sophisticated
but relatively slow versions of SVM, namely, the nonlinear SVM. The complexity
of nonlinear SVM solvers and the number of elements in the kernel matrix
quadratically increases with the number of samples in training data. Therefore,
both runtime and memory requirements are negatively affected. Moreover, the
parameter fitting has extra kernel parameters to tune, which exacerbate the
runtime even further. This paper proposes an adaptive multilevel learning
framework for the nonlinear SVM, which addresses these challenges, improves the
classification quality across the refinement process, and leverages
multi-threaded parallel processing for better performance. The integration of
parameter fitting in the hierarchical learning framework and adaptive process
to stop unnecessary computation significantly reduce the running time while
increase the overall performance. The experimental results demonstrate reduced
variance on prediction over validation and test data across levels in the
hierarchy, and significant speedup compared to state-of-the-art nonlinear SVM
libraries without a decrease in the classification quality. The code is
accessible at https://github.com/esadr/amlsvm.
