Reflexive Regular Equivalence for Bipartite Data
Bibliographic record
Abstract
Bipartite data is common in data engineering and brings unique challenges, particularly when it comes to clustering tasks that impose on strong structural assumptions. This work presents an unsupervised method for assessing similarity in bipartite data. Similar to some co-clustering methods, the method is based on regular equivalence in graphs. The algorithm uses spectral properties of a bipartite adjacency matrix to estimate similarity in both dimensions. The method is reflexive in that similarity in one dimension is used to inform similarity in the other. Reflexive regular equivalence can also use the structure of transitivities -- in a network sense -- the contribution of which is controlled by the algorithm's only free-parameter, $α$. The method is completely unsupervised and can be used to validate assumptions of co-similarity, which are required but often untested, in co-clustering analyses. Three variants of the method with different normalizations are tested on synthetic data. The method is found to be robust to noise and well-suited to asymmetric co-similar structure, making it particularly informative for cluster analysis and recommendation in bipartite data of unknown structure. In experiments, the convergence and speed of the algorithm are found to be stable for different levels of noise. Real-world data from a network of malaria genes are analyzed, where the similarity produced by the reflexive method is shown to out-perform other measures' ability to correctly classify genes.
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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 | 0.013 | 0.079 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".