Fast Graph Sampling for Short Video Summarization Using Gershgorin Disc Alignment
Bibliographic record
Abstract
We study the problem of efficiently summarizing a short video into several keyframes, leveraging recent progress in fast graph sampling. Specifically, we first construct a similarity path graph (SPG) G, represented by graph Laplacian matrix L, where the similarities between adjacent frames are encoded as positive edge weights. We show that maximizing the smallest eigenvalue λmin(B) of a coefficient matrix B = diag(a) + µL, where a is the binary keyframe selection vector, is equivalent to minimizing a worst-case signal reconstruction error. We prove that, after partitioning $\mathcal{G}$ into Q sub-graphs $\left\{ {{\mathcal{G}^q}} \right\}_{q = 1}^Q$, the smallest Gershgorin circle theorem (GCT) lower bound of Q corresponding coefficient matrices—${\min _q}\lambda _{\min }^ - \left( {{{\mathbf{B}}^q}} \right)$—is a lower bound for λmin(B). This inspires a fast graph sampling algorithm to iteratively partition $\mathcal{G}$ into Q sub-graphs using Q samples (keyframes), while maximizing $\lambda _{\min }^ - \left( {{{\mathbf{B}}^q}} \right)$ for each sub-graph ${\mathcal{G}^q}$. Experimental results show that our algorithm achieves comparable video summarization performance as state-of-the-art methods, at a substantially reduced complexity.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".