A Spectral Graph Fractional Stockwell Transform for Signal Analysis
Bibliographic record
Abstract
In this paper, we introduce a fractional-order variant of the Stockwell transform, specifically designed for analyzing signals that can be represented in terms of a graph data structure and integrates the ideas of fractional Stockwell transform and spectral graph theory.The proposed transform is named the 'Spectral Graph Fractional Stockwell Transform' or 'SGFrST' for short.Fundamentally, SGFrST makes use of the graph spectral domain to extract the underlying connection patterns and network structure of complex systems.SGFrST essentially fills the gap between signal processing methods and spectral graph theory by providing a flexible instrument that allows for hitherto unheard-of levels of precision and efficiency when comprehending and interpreting signals on graph-based domains.To begin, we introduce the spectral graph Stockwell transform by modulating the graph wavelet transform.Subsequently, we extend this concept by incorporating the spectral graph wavelet operator alongside the fractional order, resulting in the SGFrST.We derive various mathematical properties associated with the SGFrST, including an inversion mechanism and an inner product theorem.The proposed transform demonstrates effective applicability across a spectrum of graph signal processing scenarios.Basically, this makes it possible to extract useful features from signals that are present on graph structures, which helps with a variety of tasks in domains such as the social sciences, neuroscience, image processing and telecommunications.These tasks include image restoration, anomaly detection, pattern identification, and classification.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 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".