Spectral Graph Learning With Core Eigenvectors Prior via Iterative GLASSO and Projection
Bibliographic record
Abstract
Before the execution of many standard graph signal processing (GSP) modules, such as compression and restoration, learning of a graph that encodes pairwise (dis)similarities in data is an important precursor. In data-starved scenarios, to reduce parameterization, previous graph learning algorithms make assumptions in the nodal domain on i) graph connectivity (e.g., edge sparsity), and/or ii) edge weights (e.g., positive edges only). In this paper, given an empirical covariance matrix$\bar{{\mathbf{C}}}$estimated from sparse data, we consider instead a spectral-domain assumption on the graph Laplacian matrix${\mathcal{L}}$: the first$K$eigenvectors (called “core” eigenvectors)$\{{\mathbf{u}}_{k}\}$of${\mathcal{L}}$are pre-selected—e.g., based on domain-specific knowledge—and only the remaining eigenvectors are learned and parameterized. We first prove that, inside a Hilbert space of real symmetric matrices, the subspace${\mathcal{H}}_{\mathbf{u}}^{+}$of positive semi-definite (PSD) matrices sharing a common set of core$K$eigenvectors$\{{\mathbf{u}}_{k}\}$is a convex cone. Inspired by the Gram-Schmidt procedure, we then construct an efficient operator to project a given positive definite (PD) matrix onto${\mathcal{H}}_{\mathbf{u}}^{+}$. Finally, we design a hybrid graphical lasso/projection algorithm to compute a locally optimal inverse Laplacian${\mathcal{L}}^{-1}\in{\mathcal{H}}_{\mathbf{u}}^{+}$given$\bar{{\mathbf{C}}}$. We apply our graph learning algorithm in two practical settings: parliamentary voting interpolation and predictive transform coding in image compression. Experiments show that our algorithm outperformed existing graph learning schemes in data-starved scenarios for both synthetic data and these two 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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.003 |
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".