Kernels and Regularization on Graphs

We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.

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