Tradeoffs between density and size in extracting dense subgraphs: a unified framework
Bibliographic record
Abstract
Extracting dense subgraphs is an important step in many graph related applications. There is a challenging struggle in exploring the tradeoffs between density and size in subgraphs extracted. More often than not, different methods aim at different specific tradeoffs between the two factors. To the best of our knowledge, no existing method can allow a user to explore the full spectrum of the tradeoffs using a single parameter. In this paper, we investigate this problem systematically. First, since the existing studies cannot find highly compact dense subgraphs, we formulate the problem of finding very dense but relatively small subgraphs. Second, we connect our problem with the existing methods and propose a unified framework that can explore the tradeoffs between density and size of dense subgraphs extracted using a hyper-parameter. We give theoretical upper and lower bounds on the hyper-parameter so that the range where the unified framework can produce non-trivial subgraphs is determined. Third, we develop an efficient quadratic programming method for the unified framework, which is a generalization and extension to the existing methods. We show that optimizing the unified framework is essentially a relaxation of the maximization of a family of density functions. Last, we report a systematic empirical study to verify our findings.
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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 | 0.042 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.014 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.003 |
| 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".