Abstract
Simplicial complexes provide a useful framework of higher-order networks that model co-occurrences and interactions among more than two elements, and are also equipped with a mathematical foundation in algebraic topology. In this paper, we investigate the temporal growth processes of simplicial complexes derived from human activities and communication on social media from a perspective of burst vertices. First, we empirically show that most of new simplices contain burst vertices, while for each new simplex containing a burst vertex, its vertices other than the corresponding burst vertex do not necessarily co-occur with the burst vertex itself within the not so distant past. We thus examine the problem of finding which burst vertex is contained in a new simplex from the occurrence history of burst vertices. In particular, we focus on analyzing the influence of the occurrence events of burst vertices in terms of time-decays. To this end, we propose a probabilistic model incorporating a log-normal-like time-decay factor and give its learning method. Using real social media datasets, we demonstrate the significance of the proposed model in terms of prediction performance, and uncover the time-decay effects of burst vertices in the occurrence of new simplices by applying the proposed model.
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Notes
- 1.
In our experiments, we set \(\Delta t_1\) to one week (seven days) and \(\Delta t_2\) to \(2 \Delta t_1\).
- 2.
In our experiments, we set \(\Delta t_0\) to four weeks (28 days).
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- 4.
First, we removed general-purpose ingredients for Japanese food such as soy sauce, salt, sugar, water, edible oil, and so on. Furthermore, we extracted the ingredients appearing in five or more recipes.
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Acknowledgements
This work was supported in part by JSPS KAKENHI Grant Number JP21K12152. The Cookpad dataset we used in this paper was provided by Cookpad Inc. and National Institute of Informatics.
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Takai, C., Kumano, M., Kimura, M. (2024). Analyzing Temporal Influence of Burst Vertices in Growing Social Simplicial Complexes. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1144. Springer, Cham. https://doi.org/10.1007/978-3-031-53503-1_1
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