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 positive temperature parameter T. To this end, the randomized shortest path (RSP) formalism 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 \(T \rightarrow 0\). 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.

这项工作阐述了以下重要问题：（1）设计最佳的随机路由策略，以从加权有向图G上的源注释s到达目标节点t，以及（2）定义在成本最低的节点之间插值的节点之间的距离度量。上最佳运动）和通勤成本（基于随机游走ģ），这取决于正温度参数Ť。为此，根据Tsallis散度正则化而不是Kullback-Leibler散度对随机最短路径（RSP）形式主义进行了表述。此更改的主要结果是，当T减小，因此当\（T \ rightarrow 0 \）时，在G上导致收敛到最小代价有向无环图的稀疏随机游动。对节点聚类和半监督分类任务的实验比较表明，基于预期路由成本得出的相异性度量提供了最新的结果。因此，稀疏RSP是一个有希望的图形运动模型，平衡了稀疏开发和探索。