Topic-Based Analysis of Structural Transitions of Temporal Hypergraphs Derived from Recipe Sharing Sites

We analyze a recipe stream created on a social media site dedicated to sharing homemade recipes in terms of a temporal hypergraph over a set of ingredients. Unlike the previous studies for transition analysis of temporal higher-order networks, we propose a novel analysis method based on topics and projected graphs to effectively characterize the structural transitions of the temporal hypergraph immediately before and after the occurrences of hyperedges. First, we propose a probabilistic model to extract the topics of hyperedges on the basis of the trends and seasonality of recipes, and present its Bayesian inference method. Next, we propose employing the projected graph of the entire hypergraph, and examining whether each of its main edges is present or not in the temporal hypergraph, both immediately before and after the occurrences of hyperedges for each topic. Using real data of a Japanese recipe sharing site, we empirically demonstrate the effectiveness of the proposed analysis method, and reveal several interesting properties in the evolution of Japanese homemade recipes.