Analysis of Correlation Matrices Using Scale-Invariant Common Principal Component Models and a Hierarchy of Relationships Between Correlation Matrices
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Bibliographic record
Abstract
In this article, we demonstrate that the scale-invariant common principal component (CPC) model previously developed in the literature is in fact not scale invariant and cannot be used to analyze correlation matrices. To fill this gap, the correct formulation of the scale-invariant CPC model is provided, and an offspring scale-invariant CPC model is defined. Based on a series of scale-invariant CPC models, a hierarchy of relationships between correlation matrices is established. We illustrate the proposed scale-invariant CPC models with two numeric examples, and spend efforts on the interpretation of the common PCs in the second example. Some suggestions are given at the end regarding the software implementation of the scale-invariant CPC models.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.000 | 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 it