Takeaki Uno

Kazuki Nakajima, Yuya Sasaki, Takeaki Uno et al.

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale organization, yet their extension to hypergraphs involves a trade-off between expressive power and computational complexity. A recent simplification, a single-order model, mitigates this complexity by assuming a single affinity pattern governs interactions of all orders. This universal assumption, however, may overlook order-dependent structural details. Here, we propose a framework that relaxes this assumption by introducing a multi-order block structure, in which different affinity patterns govern distinct subsets of interaction orders. Our framework is based on a multi-order stochastic block model and searches for the optimal partition of the set of interaction orders that maximizes out-of-sample hyperlink prediction performance. Analyzing a diverse range of real-world networks, we find that multi-order block structures are prevalent. Accounting for them not only yields better predictive performance over the single-order model but also uncovers sharper, more interpretable mesoscale organization. Our findings reveal that order-dependent mechanisms are a key feature of the mesoscale organization of real-world higher-order networks.

Kazuki Nakajima, Takeaki Uno

Hypergraphs represent complex systems involving interactions among more than two entities and allow the investigation of higher-order structure and dynamics in complex systems. Node attribute data, which often accompanies network data, can enhance the inference of community structure in complex systems. While mixed-membership stochastic block models have been employed to infer community structure in hypergraphs, they complicate the visualization and interpretation of inferred community structure by assuming that nodes may possess soft community memberships. In this study, we propose a framework, HyperNEO, that combines mixed-membership stochastic block models for hypergraphs with dimensionality reduction methods. Our approach generates a node layout that largely preserves the community memberships of nodes. We evaluate our framework on both synthetic and empirical hypergraphs with node attributes. We expect our framework will broaden the investigation and understanding of higher-order community structure in complex systems.

Takeaki Uno, Hiroki Maegawa, Takanobu Nakahara et al.

We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at sparse parts. The problem formulation of micro-clustering is non-trivial. Clique mining in a similarity graph is a typical approach, but it results in a huge number of cliques that are of many similar cliques. We propose a new concept data polishing. The cause of huge solutions can be considered that the groups are not clear in the data, that is, the boundaries of the groups are not clear, because of noise, uncertainty, lie, lack, etc. Data polishing clarifies the groups by perturbating the data. Specifically, dense subgraphs that would correspond to clusters are replaced by cliques. The clusters are clarified as maximal cliques, thus the number of maximal cliques will be drastically reduced. We also propose an efficient algorithm applicable even for large scale data. Computational experiments showed the efficiency of our algorithm, i.e., the number of solutions is small, (e.g., 1,000), the members of each group are deeply related, and the computation time is short.