Abstract
We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than those other algorithms are to over training. This issue is related to the generalisation of a multivariate algorithm (MVA); a problem that has often been overlooked in particle physics. We discuss cross validation and how this can be used to improve the generalisation of a MVA in the context of High Energy Physics analyses. The examples presented use the Toolkit for Multivariate Analysis (TMVA) based on ROOT and describe our improvements to the SVM functionality and new tools introduced for cross validation within this framework.
Highlights
Machine learning methods are used widely within High Energy Physics (HEP)
One promising approach, used extensively outside of HEP for applications such as handwriting recognition, is that of Support Vector Machines (SVMs), a supervised learning model used with associated learning algorithms for multivariate analysis (MVA)
Developed originally in the 1960s, with the current standard version proposed in 1995 [1], SVMs aim to classify data points using a maximal margin hyperplane mapped from a linear classification problem to a possibly infinite dimensional hyperspace
Summary
Machine learning methods are used widely within High Energy Physics (HEP). One promising approach, used extensively outside of HEP for applications such as handwriting recognition, is that of Support Vector Machines (SVMs), a supervised learning model used with associated learning algorithms for multivariate analysis (MVA). Developed originally in the 1960s, with the current standard version proposed in 1995 [1], SVMs aim to classify data points using a maximal margin hyperplane mapped from a linear classification problem to a possibly infinite dimensional hyperspace. This means SVMs, like other MVA classifiers, have a number of free parameters which need to be tuned on a case by case basis. Considering two points that lie closest to the hyperplane referred to as support vectors (SVs), x+ and x , with functio⇣nDal marginEs ofD +1 andE⌘1 respectively, the geometric margin can be defined as
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