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Typically, nonlinear Support Vector Machines (SVMs) produce significantlyhigher classification quality when compared to linear ones but, at the sametime, their computational complexity is prohibitive for large-scale datasets:this drawback is essentially related to the necessity to store and manipulatelarge, dense and unstructured kernel matrices. Despite the fact that at thecore of training a SVM there is a \textit{simple} convex optimization problem,the presence of kernel matrices is responsible for dramatic performancereduction, making SVMs unworkably slow for large problems. Aiming to anefficient solution of large-scale nonlinear SVM problems, we propose the use ofthe \textit{Alternating Direction Method of Multipliers} coupled with\textit{Hierarchically Semi-Separable} (HSS) kernel approximations. As shown inthis work, the detailed analysis of the interaction among their algorithmiccomponents unveils a particularly efficient framework and indeed, the presentedexperimental results demonstrate a significant speed-up when compared to the\textit{state-of-the-art} nonlinear SVM libraries (without significantlyaffecting the classification accuracy).

Training very large scale nonlinear SVMs using Alternating Direction  Method of Multipliers coupled with the Hierarchically Semi-Separable kernel  approximations