Evaluation for the performance of learning algorithm has been the main thread of theoretical research of machine learning. The performance of the regularized regression algorithm based on independent and identically distributed（i.i.d.） samples has been researched by a large number of references. In the present paper we provide the convergence rates for the performance of regularized regression based on the inputs of p-order Markov chains.
两步降维的核主成份分析(kernel principal component analysis,KPCA)+线性判别式分析(linear discriminantanalysis,LDA)法中,第一步KPCA变换阵的选取影响数据的分类结果。对线性不可分问题首先研究了正定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;其次,将正定核推广到不定核,研究了不定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;最后通过实验加以分析和验证。
The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β） （x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β） 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.
