Temporal network analysis using zigzag persistence

Myers, Audun; Muñoz, David; Khasawneh, Firas A.; Munch, Elizabeth

doi:10.1140/epjds/s13688-023-00379-5

Cited by 10 publications

(4 citation statements)

References 54 publications

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“…This shows that our framework is general, flexible and applicable for a wide variety of problems and contexts. Note that the sets of the symmetric difference {K t Δ L t } do not form a filtration nor a zigzag filtration [Myers et al, 2023, Sec 2.2], [Carlsson and Silva, 2008].…”

Section: Methodsunclassified

Comparing structure and dynamics of transition graphs by the symmetric difference metric over an edge-filtration

Pascual,

Salbu,

Renz

et al. 2024

Preprint

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Transition graphs or transition diagrams, describing the rates and probabilities with which a system changes between discrete states, are common throughout the sciences. In many cases, parameterisations of transition graphs are inferred from different datasets, for example in the context of Markov or hidden Markov models. An important task for followup analysis is to find efficient and effective ways to compare transition graphs with different parameterisations. Here, we introduce the Weight-Filtration Comparison Curve (WFCC), an approach by which the differences between two or more parameterisations of a transition graph can be quantified and compared. Borrowing from topological data analysis, the WFCC allows graphs learned from different datasets and/or null models to be systematically compared, and differences in both the fine- and coarse-grained structure and dynamics of transition graphs to be quantitatively assessed. We demonstrate WFCC with simple illustrative cases and real-world cases of transition graphs inferred from global data on the evolution of antimicrobial resistance in different countries, showing how different inferred dynamics, and different levels of uncertainty, are reported by structural aspects of these comparison curves.

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Section: Methodsunclassified

Comparing structure and dynamics of transition graphs by the symmetric difference metric over an edge-filtration

Pascual,

Salbu,

Renz

et al. 2024

Preprint

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“…As discussed earlier, our problem can also be used in the path route applications. In addition, our problem seeks to fnd the connected minimum-weighted tree in temporal graphs, which is unlike the subgraph mining in temporal networks [7,10,13,[48][49][50]. In general, our algorithm considers the search based on labels/keywords in a large graph, a method that is similar to the keyword search in large graphs [51] and the keyword-aware route search [52].…”

Section: Related Workmentioning

confidence: 99%

An Efficient Dynamic Programming Algorithm for Finding Group Steiner Trees in Temporal Graphs

Ge,

Chen,

Kong

et al. 2023

International Journal of Intelligent Systems

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The computation of a group Steiner tree (GST) in various types of graph networks, such as social network and transportation network, is a fundamental graph problem in graphs, with important applications. In these graphs, time is a common and necessary dimension, for example, time information in social network can be the time when a user sends a message to another user. Graphs with time information can be called temporal graphs. However, few studies have been conducted on GST in terms of temporal graphs. This study analyzes the computation of GST for temporal graphs, i.e., the computation of temporal GST (TGST), which is shown to be an NP-hard problem. We propose an efficient solution based on a dynamic programming algorithm for our problem. This study adopts new optimization techniques, including graph simplification, state pruning, and A ∗ search, are adopted to dramatically reduce the algorithm search space. Moreover, we consider three extensions for our problem, namely the TGST with unspecified tree root, the progressive search of TGST, and the top-N search of TGST. Results of the experimental study performed on real temporal networks verify the efficiency and effectiveness of our algorithms.

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“…Dynamic TDA methods have been previously applied to analysing aggregation models, fish swarms and temporal networks [ 31 , 38 , 39 ]. However, zigzag persistence of dynamic data for larger systems was computationally out of reach until recently [ 40 ].…”

Section: Introductionmentioning

confidence: 99%

Zigzag persistence for coral reef resilience using a stochastic spatial model

McDonald,

Neuhausler,

Robinson

et al. 2023

J. R. Soc. Interface.

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A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterizing spatio-temporal data and understanding how changes at the local scale affect global dynamics/behaviour. Here, we extend a well-studied temporal mathematical model of coral reef dynamics to include stochastic and spatial interactions and generate data to study different ecological scenarios. We present descriptors to characterize patterns in heterogeneous spatio-temporal data surpassing spatially averaged measures. We apply these descriptors to simulated coral data and demonstrate the utility of two topological data analysis techniques—persistent homology and zigzag persistence—for characterizing mechanisms of reef resilience. We show that the introduction of local competition between species leads to the appearance of coral clusters in the reef. We use our analyses to distinguish temporal dynamics stemming from different initial configurations of coral, showing that the neighbourhood composition of coral sites determines their long-term survival. Using zigzag persistence, we determine which spatial configurations protect coral from extinction in different environments. Finally, we apply this toolkit of multi-scale methods to empirical coral reef data, which distinguish spatio-temporal reef dynamics in different locations, and demonstrate the applicability to a range of datasets.

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Temporal network analysis using zigzag persistence

Cited by 10 publications

References 54 publications

Comparing structure and dynamics of transition graphs by the symmetric difference metric over an edge-filtration

Comparing structure and dynamics of transition graphs by the symmetric difference metric over an edge-filtration

An Efficient Dynamic Programming Algorithm for Finding Group Steiner Trees in Temporal Graphs

Zigzag persistence for coral reef resilience using a stochastic spatial model

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