  We review the concept of Support Vector Machines (SVMs) and discuss examples
of their use in a number of scenarios. Several SVM implementations have been
used in HEP and we exemplify this algorithm using the Toolkit for Multivariate
Analysis (TMVA) implementation. We discuss examples relevant to HEP including
background suppression for $H\to\tau^+\tau^-$ at the LHC with several different
kernel functions. Performance benchmarking leads to the issue of generalisation
of hyper-parameter selection. The avoidance of fine tuning (over training or
over fitting) in MVA hyper-parameter optimisation, i.e. the ability to ensure
generalised performance of an MVA that is independent of the training,
validation and test samples, is of utmost importance. We discuss this issue and
compare and contrast performance of hold-out and k-fold cross-validation. We
have extended the SVM functionality and introduced tools to facilitate cross
validation in TMVA and present results based on these improvements.
