Improvements to the non‐linear principal component analysis method, with applications to ENSO and QBO
Bibliographic record
Abstract
Two improvements to the Non‐linear Principal Component Analysis (NLPCA) method are presented. In the normal application of this method, a non‐linear curve C is found that best fits the data. The method provides a projection function mapping from the data space to the curve C. However, this projection function is faulty in that points in the data space are generally not projected onto their closest neighbours on C. Here, a new projection function is introduced which ensures that the data points are projected onto their closest neighbours on C, resulting in an increase in the amount of variance explained by the NLPCA mode. This is illustrated by an analysis of the sea surface temperature anomaly data from the tropical Pacific, where the El Niño‐Southern Oscillation (ENSO) phenomenon is manifested. A second shortcoming of the NLPCA method is that the curve C comes with a parametrization which is arbitrary and has no physical interpretation. Here, the curve is re‐parametrized by arc length. This allows the computation of more meaningful time series, which we illustrate through an analysis of the Quasi‐Biennial Oscillation (QBO) in the equatorial stratospheric zonal wind data.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".