期刊名称：International Journal of Artificial Intelligence & Applications (IJAIA)
印刷版ISSN：0976-2191
电子版ISSN：0975-900X
出版年度：2017
卷号：8
期号：5
页码：1
DOI：10.5121/ijaia.2017.8506
出版社：Academy & Industry Research Collaboration Center (AIRCC)
摘要：Manifold regularization is an approach which exploits the geometry of the marginal distri-bution. The main goal of this paper is to analyze the convergence issues of such regularizationalgorithms in learning theory. We propose a more general multi-penalty framework and es-tablish the optimal convergence rates under the general smoothness assumption. We study atheoretical analysis of the performance of the multi-penalty regularization over the reproduc-ing kernel Hilbert space. We discuss the error estimates of the regularization schemes undersome prior assumptions for the joint probability measure on the sample space. We analyze theconvergence rates of learning algorithms measured in the norm in reproducing kernel Hilbertspace and in the norm in Hilbert space of square-integrable functions. The convergence issuesfor the learning algorithms are discussed in probabilistic sense by exponential tail inequalities.In order to optimize the regularization functional, one of the crucial issue is to select regular-ization parameters to ensure good performance of the solution. We propose a new parameterchoice rule \the penalty balancing principle" based on augmented Tikhonov regularization forthe choice of regularization parameters. The superiority of multi-penalty regularization oversingle-penalty regularization is shown using the academic example and moon data set.
