On Convergence of the Method of Relaxations, an Application to Learning on a Graph.
Résumé
We present a semi-supervised algorithm to learn an interpolating function with minimal Laplacian semi-norm on a graph. This algorithm is directly inspired by the classical 'method of relaxations' used in physics to get discrete approximate solutions to the Dirichlet problem. We argue that this method is actually a gradient descent minimizing the energy of an interpolating function on the graph. Besides it converges linearly in the number of steps, with a convergence constant bounded with respect to simple characteristics of the graph. As opposed to inversion-based kernel methods on graph, this algorithm can be efficiently implemented to deal with large, complex graphs.
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