Graph Learning and Optimization for Irregular-Structured Signal Processing
Bibliographic record
Abstract
Graph Signal Processing (GSP) extends harmonic analysis tools, such as Fourier transforms and wavelets, to discrete signals defined on finite graphs, enabling tasks like signal denoising, prediction, and interpolation on irregular domains. A critical first step in GSP is to learn an appropriate graph that captures pairwise similarities or correlations inherent in the data, ensuring that subsequent graph-based filtering effectively leverages local structure for improved performance. However, most existing graph learning methods assume static relationships, while real-world interactions often evolve over time. To address this problem, this thesis proposes a slowly time-varying graph learning framework that models the difference between consecutive adjacency matrices as a low-rank matrix. This approach accommodates gradual shifts in node-to-node similarities over time, enabling efficient graph updates with low computational overhead while maintaining alignment with the underlying data. Beyond graph construction, the challenge of dense or complete graphs often arises, particularly in large-scale applications where representing all possible edges is computationally prohibitive. To address this issue, this thesis introduces a sparsification method guided by the Fiedler number, the second smallest eigenvalue of the Laplacian, which quantifies graph connectivity. By removing edges that minimally affect the Fiedler number, the resulting sparser graph preserves essential connectivity while significantly reducing training and inference costs for deep learning models (e.g, graph convolutional networks (GCNs)). Together, these contributions provide a flexible and computationally efficient approach to GSP in dynamic and large-scale graph settings.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".