Abstract:Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that is scalable and efficient. We map t… Show more
“…A promising approach is that of optimal transport theory. Recent studies [25,26] have shown that this theoretical formalism can be adapted to address multicommodity scenarios, generalizing well-established results for unicommodity models [27][28][29][30][31][32][33]. The works of Lonardi et al [25] and Bonifaci et al [26] focus on a theoretical characterization of the problem, drawing a formal connection between optimal transport and an equivalent dynamical system that is formulated in terms of physical quantities like conductivities and fluxes.…”
Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions-quantities determining the interaction between passengers-in the dynamics implementing the optimal transport formulation. Particularly, we compare a theoretically-grounded response function with one that is intuitive for settings involving transportation of passengers, albeit lacking theoretical justifications. We investigate these two modeling choices on the Paris metro and analyze how they reflect on passengers' fluxes. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.
“…A promising approach is that of optimal transport theory. Recent studies [25,26] have shown that this theoretical formalism can be adapted to address multicommodity scenarios, generalizing well-established results for unicommodity models [27][28][29][30][31][32][33]. The works of Lonardi et al [25] and Bonifaci et al [26] focus on a theoretical characterization of the problem, drawing a formal connection between optimal transport and an equivalent dynamical system that is formulated in terms of physical quantities like conductivities and fluxes.…”
Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions-quantities determining the interaction between passengers-in the dynamics implementing the optimal transport formulation. Particularly, we compare a theoretically-grounded response function with one that is intuitive for settings involving transportation of passengers, albeit lacking theoretical justifications. We investigate these two modeling choices on the Paris metro and analyze how they reflect on passengers' fluxes. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.
“…When fewer edges are used, hence we observe branched transportation, and the -Wasserstein cost coincides with a branched transport distance 25 , 53 . The idea of tuning to interpolate between various transportation regimes has been used in several works and engineering applications 27 , 54 – 59 . Figure 2 Visualization of how impacts intra-community and inter-community edge weights.…”
Section: β-Wasserstein Community Detection Algorithmmentioning
Detecting communities in networks is important in various domains of applications. While a variety of methods exist to perform this task, recent efforts propose Optimal Transport (OT) principles combined with the geometric notion of Ollivier–Ricci curvature to classify nodes into groups by rigorously comparing the information encoded into nodes’ neighborhoods. We present an OT-based approach that exploits recent advances in OT theory to allow tuning between different transportation regimes. This allows for better control of the information shared between nodes’ neighborhoods. As a result, our model can flexibly capture different types of network structures and thus increase performance accuracy in recovering communities, compared to standard OT-based formulations. We test the performance of our algorithm on both synthetic and real networks, achieving a comparable or better performance than other OT-based methods in the former case, while finding communities that better represent node metadata in real data. This pushes further our understanding of geometric approaches in their ability to capture patterns in complex networks.
“…When β > 1 fewer edges are used, hence we observe branched transportation, and the β -Wasserstein cost coincides with a branched transport distance 21,36 . The idea of tuning β to interpolate between various transportation regimes has been used in several works and engineering applications 23,[37][38][39][40][41][42] .…”
Section: β -Wasserstein Community Detection Algorithmmentioning
Detecting communities in networks is important in various domains of applications. While a variety of methods exists to perform this task, recent efforts propose Optimal Transport (OT) principles combined with the geometric notion of Ollivier-Ricci curvature to classify nodes into groups by rigorously comparing the information encoded into nodes' neighborhoods. We present an OT-based approach that exploits recent advances in OT theory to allow tuning for traffic penalization, which enforces different transportation schemes. As a result, our model can flexibly capture different scenarios and thus increase performance accuracy in recovering communities, compared to standard OT-based formulations. We test the performance of our algorithm in both synthetic and real networks, achieving a comparable or better performance than other OT-based methods in the former case, while finding communities more aligned with node metadata in real data. This pushes further our understanding of geometric approaches in their ability to capture patterns in complex networks.
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