Efficient modeling of higher-order dependencies in networks: from algorithm to application for anomaly detection

Abstract

Complex systems, represented as dynamic networks, comprise of components that influence each other via direct and/or indirect interactions. Recent research has shown the importance of using Higher-Order Networks (HONs) for modeling and analyzing such complex systems, as the typical Markovian assumption in developing the First Order Network (FON) can be limiting. This higher-order network representation not only creates a more accurate representation of the underlying complex system, but also leads to more accurate network analysis. In this paper, we first present a scalable and accurate model, , for higher-order network representation of data derived from a complex system with various orders of dependencies. Then, we show that this higher-order network representation modeled by is significantly more accurate in identifying anomalies than FON, demonstrating a need for the higher-order network representation and modeling of complex systems for deriving meaningful conclusions.

Global port survey quantifies commercial shipping’s effect on biodiversity

“…We provide in situ evidence of the relative effects of shipping and the environment on biological homogenization at the global scale. We also reveal the importance of stepping-stone connections for species spread through the global shipping network, which highlights the need to consider the whole shipping network to predict species spread (Saebi, Xu, Kaplan, et al, 2020;Xu et al, 2016). While it is generally accepted that differences among ship types result in unequal risks of species transfer (Davidson et al, 2018;Drake & Lodge, 2004), including ship and voyage parameters influencing ballast discharge in our models had no significant effect on our ability to explain the biological similarities between ports.…”

“…As a result, the remaining ballast water discharged by the ship at the intermediate stops poses the risk of NIS transfer from the original port to the intermediate stops. To account for more such patterns of NIS spread, we followed the approach of (Saebi, Xu, Grey, et al, 2020;Saebi, Xu, Kaplan, et al, 2020) to obtain 4 different traffic-and ballast-associated risks. We used eight years of shipping data from 1997 to 2018 obtained from Lloyd's List Intelligence, an Informa Group Company (LLI, New York, NY, USA).…”

“…Here we use a global environmental DNA metabarcoding survey to evaluate four models of ship-borne eukaryotic species spread risk. We show that eDNA analysis of port water samples, together with global data on environmental conditions and shipping traffic, enables route-specific risk analyses of ship-borne species spread (Porter & Hajibabaei, 2018;Saebi, Xu, Kaplan, et al, 2020;Thomsen & Willerslev, 2015;Xu et al, 2016). By implementing a standardized and efficient eDNA port survey method (Grey et al, 2018) we identified biological similarities between 19 ports and related them to four different risk estimates of ship-mediated species transport, while concurrently considering the effects of environmental similarity (Keller et al, 2011) and biogeography (Costello et al, 2017) on global community compositions.…”

“…Our four alternative shipping-risk estimates derived from long-term ship traffic data consider two different aspects of the species spread risk along routes in the global shipping network. The first aspect considered route spread risk as either function of the number of ships traveling between two ports ("traffic risk") or as a function describing the amount of ballast water ("ballast risk") transported between ports, based on correlations between ballast discharge volume and probability with ship size, ship type, and voyage time (Saebi, Xu, Grey, et al, 2020;Saebi, Xu, Kaplan, et al, 2020). The second aspect considered the importance of either direct port-to-port voyages ("direct connection risk") or indirect connections through intermediary ports ("steppingstone connection risk").…”

Network analysis of ballast-mediated species transfer reveals important introduction and dispersal patterns in the Arctic

“…www.nature.com/scientificreports/ www.nature.com/scientificreports/ The example of considered SF-HON structure and dynamics outlined above is likely to be very important to species dispersal: ship movements demonstrate up to fifth order dependency which can only be effectively captured by higher-order network modeling 30,31 . Moreover, higher-order structures influence clustering, ranking, diffusion, network representation, and anomaly detection in networks 30,[39][40][41] . However, SF-HON structure and its implications have not been studied for Arctic shipping.…”