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arXiv · 2007.00419

Sparse Randomized Shortest Paths Routing with Tsallis Divergence Regularization

Pierre Leleux·Sylvain Courtain·Guillaume Guex·Marco Saerens
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Abstract

This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes interpolating between the least cost (based on optimal movements) and the commute-cost (based on a random walk on G), depending on a temperature parameter T. To this end, the randomized shortest path formalism (RSP, [2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead of Kullback-Leibler divergence. The main consequence of this change is that the resulting routing policy (local transition probabilities) becomes sparser when T decreases, therefore inducing a sparse random walk on G converging to the least-cost directed acyclic graph when T tends to 0. Experimental comparisons on node clustering and semi-supervised classification tasks show that the derived dissimilarity measures based on expected routing costs provide state-of-the-art results. The sparse RSP is therefore a promising model of movements on a graph, balancing sparse exploitation and exploration in an optimal way.

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Pierre Leleux, Sylvain Courtain, Guillaume Guex, Marco Saerens. 2020-07-01. Sparse Randomized Shortest Paths Routing with Tsallis Divergence Regularization. https://doi.org/10.1007/s10618-021-00742-y

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