arXiv subjects

Quang Nguyen

Publications and source records attributed to Quang Nguyen.

39 records · Page 3Linked to original sources

arXiv2021

On Robust Optimal Transport: Computational Complexity and Barycenter Computation

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost of robust optimal transport in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, in which $n$ is the number of supports of the probability distributions and $\varepsilon$ is the desired error. Furthermore, we investigate a fixed-support robust barycenter problem between $m$ discrete probability distributions with at most $n$ number of supports and develop an approximating algorithm based on iterative Bregman projections (IBP). For the specific case $m = 2$, we show that this algorithm can approximate the optimal barycenter value in $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon})$ time, thus being better than the previous complexity $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon^2})$ of the IBP algorithm for approximating the Wasserstein barycenter.

cs.LG↗

arXiv2020

Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi-Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that higher level of modularity decreases the model network robustness under both attack strategies, i.e. model network with higher community structure showed faster LCC disruption when subjected to node removal. Very interesting, we find that when model networks showed non-modular structure or low modularity, the degree-based (ID) is more effective than the betweenness-based node attack strategy (IB). Conversely, in the case the model network present higher modularity, the IB strategies becomes clearly the most effective to fragment the LCC. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks under IB node attack strategy (p-value< 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to betwenness-based node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

physics.soc-ph↗

arXiv2020

New nodes attack strategies for real complex weighted networks

In this work we introduce a new nodes attack strategy removing nodes with highest conditional weighted betweenness centrality (CondWBet). We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network in addition to the commonly used binary-topological measure, the largest connected cluster (LCC). We find that the recently proposed conditional betweenness strategy (CondBet) (Nguyen et al. 2019) is the best to fragment the LCC in all cases. Further, we find that the introduced CondWBet strategy is the best to decrease the network efficiency (WEFF) in 3 out of 5 cases. Last, CondWBet is be the most effective strategy to reduce WEFF at the beginning of the removal process whereas the Strength that removes nodes with highest link weights first, shows the highest efficacy in the final phase of the removal process when the network is broken in many small clusters. These last outcomes would suggest that a better attacking strategy could be a combination of the CondWBet and Strength strategies

physics.soc-ph↗