Nowadays　most　of　the　current　kernel　learning　approaches　are　showing　good　results　in　small　datasets　and　fail　to　scale　to　large　ones.　As　such,　it　is　necessary　to　develop　faster　kernel　optimization　algorithms　that　perform　better　with　larger　datasets,　especially,　for　the　Big　Data　applications.　This　paper　presents　a　novel　fast　method　to　optimize　the　Gaussian　kernel　function　for　two-class　pattern　classification　tasks,　where　it　is　desirable　for　the　kernel　machines　to　use　an　optimized　kernel　that　adapts　well　to　the　input　data　and　the　learning　tasks.　We　propose　to　optimize　the　Gaussian　kernel　function　by　using　the　formulated　kernel　target　alignment　criterion.　By　adopting　the　Euler-Maclaurin　formula　and　the　local　and　global　extremal　properties　of　the　approximate　kernel　separability　criterion,　the　approximate　criterion　function　can　be　proved　to　have　a　determined　global　minimum　point.　Thus,　when　the　approximate　criterion　function　is　a　sufficient　approximation　of　the　criterion　function,　through　using　a　Newton-based　algorithm,　the　proposed　optimization　is　simply　solved　without　being　repeated　the　searching　procedure　with　different　starting　points　to　locate　the　best　local　minimum.　The　proposed　method　is　evaluated　on　thirteen　data　sets　with　three　Gaussian-kernel-based　learning　algorithms.　The　experimental　results　show　that　the　criterion　function　has　the　determined　global　minimum　point　for　the　all　thirteen　data　sets,　the　proposed　method　achieves　the　best　high　time　efficiency　performance　and　the　best　overall　classification　performance.　©　2013　Elsevier　Ltd.　All　rights　reserved.