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

• URL: http://arxiv.org/abs/2108.04167v1
• Date: Mon, 9 Aug 2021 16:52:04 GMT
• Title: Training very large scale nonlinear SVMs using Alternating Direction Method of Multipliers coupled with the Hierarchically Semi-Separable kernel approximations
• Authors: S. Cipolla, J. Gondzio
• Abstract summary: nonlinear Support Vector Machines (SVMs) produce significantly higher classification quality when compared to linear ones. Their computational complexity is prohibitive for large-scale datasets.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Typically, nonlinear Support Vector Machines (SVMs) produce significantly higher classification quality when compared to linear ones but, at the same time, their computational complexity is prohibitive for large-scale datasets: this drawback is essentially related to the necessity to store and manipulate large, dense and unstructured kernel matrices. Despite the fact that at the core of training a SVM there is a \textit{simple} convex optimization problem, the presence of kernel matrices is responsible for dramatic performance reduction, making SVMs unworkably slow for large problems. Aiming to an efficient solution of large-scale nonlinear SVM problems, we propose the use of the \textit{Alternating Direction Method of Multipliers} coupled with \textit{Hierarchically Semi-Separable} (HSS) kernel approximations. As shown in this work, the detailed analysis of the interaction among their algorithmic components unveils a particularly efficient framework and indeed, the presented experimental results demonstrate a significant speed-up when compared to the \textit{state-of-the-art} nonlinear SVM libraries (without significantly affecting the classification accuracy).

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