Clustering via hypergraph modularity
Bibliographic record
Abstract
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet.In this paper, we propose a hypergraph modularity function that generalizes its well established and widely used graph counterpart measure of how clustered a network is.In order to define it properly, we generalize the Chung-Lu model for graphs to hypergraphs.We then provide the theoretical foundations to search for an optimal solution with respect to our hypergraph modularity function.A simple heuristic algorithm is described and applied to a few illustrative examples.We show that using a strict version of our proposed modularity function often leads to a solution where a smaller number of hyperedges get cut as compared to optimizing modularity of 2-section graph of a hypergraph. IntroductionAn important property of complex networks is their community structure, that is, the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters [1,2].In social networks, communities may represent groups by interest (practical application include collaborative tagging-[3]), in citation networks they correspond to related papers (see [4]), similarly in the web communities are formed by pages on related topics.Yet another example could be financial markets where we have several groups of financial instruments that might be correlated with each other in several different groups.Such groups can be represented as hyperedges and hence detection of communities in such hypergraph could lead to better understanding of dependencies between financial instruments.Hypergraphs can also be used to model transportation systems.For example in [5] the authors consider transportation system represented as a directed hypergraph.A hyperedge can represent a situation where a single stop (starting or destination point) is being serviced by several public transportation lines and vehicle types that can be differently chosen by an agent traveling within the transportation grid and communities can represent paths taken often together.Another application was presented in [6]-the authors suggest using hypergraphs to model interactions between biological cells in computational biology.Finally,in [7] one can find a discussion on how hypergraphs can be used for modeling telecommunication systems
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".