Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignment
Bibliographic record
Abstract
A basic premise in graph signal processing (GSP) is that a graph encoding pairwise (anti-)correlations of the targeted signal as edge weights is leveraged for graph filtering. Existing fast graph sampling schemes are designed and tested only for positive graphs describing positive correlations. However, there are many real-world datasets exhibiting strong anti-correlations, and thus a suitable model is a signed graph, containing both positive and negative edge weights. In this paper, we propose the first linear-time method for sampling signed graphs, centered on the concept of balanced signed graphs. Specifically, given an empirical covariance data matrix , we first learn a sparse inverse matrix , interpreted as a graph Laplacian corresponding to a signed graph . We approximate with a balanced signed graph via fast edge weight augmentation in linear time, where the eigenpairs of Laplacian for are graph frequencies. Next, we select a node subset for sampling to minimize the error of the signal interpolated from samples in two steps. We first align all Gershgorin disc left-ends of Laplacian at the smallest eigenvalue via similarity transform , leveraging a recent linear algebra theorem called Gershgorin disc perfect alignment (GDPA). We then perform sampling on using a previous fast Gershgorin disc alignment sampling (GDAS) scheme. Experiments show that our signed graph sampling method outperformed fast sampling schemes designed for positive graphs on various datasets with anti-correlations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".