A　great　number　of　dimensionality　reduction　methods　are　finally　reduced　to　solving　generalized　eigenvector　problems.　Optimization　techniques　are　promising　ways　to　solve　the　parameter　selection　problems　in　these　dimensionality　reduction　methods.　The　most　important　step　in　these　optimization　methods　is　to　compute　the　objective　function　with　respect　to　the　parameter,　which　depends　on　computing　the　gradient　and　Hessian　matrix　of　the　resulted　eigenvectors　and　eigenvalues.　In　this　paper,　we　propose　a　novel　method　to　compute　the　gradient　of　the　eigenvalues,　and　then　apply　them　to　tune　the　parameter　in　the　kernel　principal　component　analysis.　Experimental　results　on　UCI　data　sets　show　that　the　new　method　outperforms　the　original　algorithm,　especially　in　time　complexity.　©　2011　IEEE.