Distortion in Correspondence Analysis and in Taxicab Correspondence Analysis: A Comparison
Why this work is in the frame
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Bibliographic record
Abstract
Distortion is a fundamental well-studied topic in dimension reduction papers, and intimately related with the underlying intrinsic dimension of a mapping of a high dimensional data set onto a lower dimension. In this paper, we study embedding distortions produced by Correspondence Analysis and its robust l1 variant Taxicab Correspondence analysis, which are visualization methods for contingency tables. For high dimensional data, distortions in Correspondence Analysis are contractions; while distortions in Taxicab Correspondence Analysis could be contractions or stretchings. This shows that Euclidean geometry is quite rigid, because of the orthogonality property; while Taxicab geometry is quite flexible, because the orthogonality property is replaced by the conjugacy property.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.005 | 0.009 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 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 it