Here is a way to do semi-surpevised learning with kernels (and even with Random Features at the very end)

Learning with Fredholm Kernels by Qichao Que Mikhail Belkin and Yusu Wang.

In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation. Our approach fits naturally into the kernel framework and can be interpreted as constructing new data-dependent kernels, which we call Fredholm kernels. We proceed to discuss the “noise assumption” for semi-supervised learning and provide both theoretical and experimental evidences that Fredholm kernels can effectively utilize unlabeled data under the noise assumption. We demonstrate that methods based on Fredholm learning show very competitive performance inthe standard semi-supervised learning setting

The implementation is located at: https://github.com/queqichao/FredholmLearning

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