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The paper starts by introducing the background and showing the contributions. The authors then use the Zhang and Ando result showing that SSL reduces to an equivalent kernel-based supervised learning problem for the rest of the paper. In section 2 and appendix, they provide an error bound showing that minimising the spectral norm of the graph kernel matrix is a good way to improve generalisation. In section 3, they add a spectral norm regularization term to the Zhang and Ando formulation, and provide links between the error convergence and the Lovasz number of the data graph. Section 4 proposes a proximal solver, where the specificity is that it deals with the projection step approximately to handle the constraint of a cone-polytope intersection.