Randomized shortest paths with net flows and capacity constraints

Dissecting graph measure performance for node clustering in LFR parameter space

“…There are many measure benchmarking studies considering node classification and clustering for both generated graphs and real-world datasets, including [23,50,51,2,32,29,28,3,4,16,39]. Despite a large number of experimental results, an exact theory is still a matter of the future.…”

Relative Entropy-Regularized Optimal Transport on a Graph: a new algorithm and an experimental comparison

“…The introduced algorithm solving this problem provides an optimal randomized policy balancing exploitation and exploration through a simple iterative algorithm inspired by [8]. Similarly to the standard randomized shortest paths and bag-of-paths frameworks 2 , the model is monitored by a parameter θ in such a way that, when θ goes to infinity, it approximates the optimal, lowest-cost, solution to the transportation problem.…”

“…On the contrary, in the present work, the problem is rephrased within a RSP formalism ( [38]; inspired by [2]) only considering the set of paths from one single source supernode and one target supernode, both added to the original network. This rephrasing into a source-target RSP problem allows us to easily define capacity constraints on edge flows, as explained in [8], which itself allows us to reformulate the margin-constrained BoP on a graph problem into a capacity constrained RSP problem which has its own merits, for instance allowing additional flow capacity constraints. As an application, the margin-constrained bag-of-paths surprisal distance measure between nodes [23] is derived within the new formalism.…”

“…To summarize, the predominant benefit here lies in the fact that this new formulation (in comparison to previous formulations [21,23] solving the same problem) can easily accommodate flow capacity constraints, which frequently appear in real-world applications [1]. Indeed, because the problem is transformed into a RSP single sourcesingle target framework, it suffices to follow the procedure introduced in [8] for dealing with both the margin and the capacity constraints. The new algorithm therefore solves the relative entropy-regularized minimum expected cost flow with capacity constraints problem on a graph.…”

“…The main advantage of this new formulation is the fact that it can easily accommodate edge flow capacity constraints which commonly occur in real-world problems. The resulting optimal routing policy, i.e., the probability distribution of following an edge in each node, is Markovian and is computed by constraining the input and output flows to the prescribed marginal probabilities thanks to a variant of the algorithm developed in [8]. Besides, experimental comparisons with other recently developed techniques show that the distance measure between nodes derived from the introduced model provides competitive results on semi-supervised classification tasks.…”