A measurement of the top quark pair-production cross section in the $\mathrm{lepton}+\text{jets}$ decay channel is presented. It is based on $4.6\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ $pp$ collision data collected during 2011 by the ATLAS experiment at the CERN Large Hadron Collider. A three-class, multidimensional event classifier based on support vector machines is used to differentiate $t\overline{t}$ events from backgrounds. The $t\overline{t}$ production cross section is found to be ${\ensuremath{\sigma}}_{t\overline{t}}=168.5\ifmmode\pm\else\textpm\fi{}0.7(\mathrm{stat}){\text{ }}_{\ensuremath{-}5.9}^{+6.2}(\mathrm{syst}){\text{ }}_{\ensuremath{-}3.2}^{+3.4}(\mathrm{lumi})\text{ }\text{ }\mathrm{pb}$. The result is consistent with the Standard Model prediction based on QCD calculations at next-to-next-to-leading order.