Bipartite Graph Approximation by Eigenvalue Optimization
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Graphs are a powerful tool for representing entities and their relationships. Current advances in graph signal processing have made it possible to analyze graph-based data more effectively. Recent research show that, to ensure critical sampling, manyfilterbank design algorithms are only applicable to bipartite graphs. However, general graph signals may not exist on a bipartite graph structure. To overcome this difficulty, we propose in this paper a novel algorithm to find a bipartite approximation to the original non-bipartite graph while preserving its global structure. To achieve this goal, the original bipartite graph approximation (BGA) problem is constructed based on eigenvalue optimization of adjacency matrix, which is then relaxed so as to obtain a closed-form solution. We introduce the alternating direction method of multipliers (ADMM) to achieve a single bipartite graph or a set of edge-disjoint bipartite subgraphs that approximates the original graph. Additionally, we develop a distributed version of the BGA to address the computational challenges when processing large-scale graphs. Experimental results demonstrate the effectiveness of the proposed method and suggest it as a promising alternative approach for bipartite graph decomposition.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.007 |
| Open science | 0.000 | 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 it