Generalization analysis of fredholm kernel regularized classifiers

Recently, a new framework, Fredholm learning,was proposed for semisupervisedlearning problems based on solving a regularized Fredholm integralequation. It allows a natural way to incorporate unlabeled datainto learning algorithms to improve their prediction performance. Despiterapid progress on implementable algorithms with theoretical guarantees,the generalization ability of Fredholm kernel learning has notbeen studied. In this letter, we focus on investigating the generalizationperformance of a family of classification algorithms, referred to asFredholm kernel regularized classifiers.We prove that the correspondinglearning rate can achieve O(l^-1) (l is the number of labeled samples) ina limiting case. In addition, a representer theorem is provided for theproposed regularized scheme, which underlies its applications.