Linear　discriminant　analysis　(LDA)　as　a　classical　supervised　dimensionality　reduction　method　has　shown　powerful　capability　in　various　image　classification　tasks.　The　purpose　of　LDA　seeks　an　optimal　linear　transformation　that　maps　the　original　data　to　a　low-dimensional　space.　Inspired　by　the　fact　that　the　kernel　trick　can　capture　the　nonlinear　similarity　of　features,　we　propose　a　novel　generalized　distance　constraint　dubbed　intra-class　and　inter-class　kernel　constraint　(IIKC).　The　proposed　IIKC　explicitly　models　the　category　kernel　distance　and　focuses　on　helping　the　original　LDA　capture　more　discriminant　features　in　order　to　further　improve　the　separability　and　magnitude　difference　between　nearby　data　points.　Our　proposed　method　with　IIKC　aims　to　achieve　maximum　category　separability　by　minimizing　the　intraclass　kernel　distances　as　well　as　maximizing　the　inter-class　kernel　distance,　simultaneously.　Extensive　experimental　results　on　six　publicly　available　benchmark　databases　illustrate　that　the　LDA-based　methods　embedded　with　the　proposed　IIKC　significantly　improve　the　discrimination　ability　and　achieve　a　better　classification　performance　than　the　original　and　state-of-the-art　LDA　algorithms.(c)　2022　Elsevier　Ltd.　All　rights　reserved.