Fractional graph-based semi-supervised learning

Graph-based semi-supervised learning for classification endorses a nice interpretation in terms of diffusive random walks, where the regularisation factor in the original optimisation formulation plays the role of a restarting probability. Recently, a new type of biased random walks for characterising certain dynamics on networks have been defined and rely on the γ-th power of the standard Laplacian matrix Lγ, with γ > 0. In particular, these processes embed long range transitions, the Levy flights, that are capable of one-step jumps between far-distant states (nodes) of the graph. The present contribution envisions to build upon these volatile random walks to propose a new version of graph based semi-supervised learning algorithms whose classification outcome could benefit from the dynamics induced by the fractional transition matrix.1