Joint Sampling and Reconstruction of Time-Varying Signals Over Directed Graphs
Bibliographic record
Abstract
Vertex-domain and temporal-domain smoothness of time-varying graph signals are cardinal properties that can be exploited for effective graph signal reconstruction from limited samples. However, existing approaches are not directly applicable when the signal's frequency occupancy changes with time. Moreover, while e.g., sensor network applications can benefit from directed graph models, the non-orthogonality of the graph eigenvectors can challenge spectral-based signal reconstruction algorithms. In this context, here we consider$K$-sparse time-varying signals with unknown frequency supports. By exploiting the smoothness of the varying graph frequency supports and employing shift operations over directed graphs, we study joint sampling of multiple varying signals based on Schur decomposition to reconstruct each signal by orthogonal frequency components. Firstly, joint frequency support of the multiple signals is identified by proposing a two-stage Individual-Joint sampling scheme. Based on the estimated frequency support, the GFT coefficients of each signal can be recovered using data collected in individual sampling stage. Greedy algorithms are proposed for vertex set selection and graph shift order selection, which enable a robust signal reconstruction against additive noise. Considering the signals in applications may be approximately$K$-sparse, we further exploit the samples in both individual and joint sampling stages and investigate the optimal signal reconstruction as a convex optimization problem with adaptive frequency support selection. The proposed optimal sampling and reconstruction algorithms outperform several existing schemes in random network and sensor network data gathering.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".