An Alternative Formulation of PCA for Process Monitoring Using Distance Correlation
Bibliographic record
Abstract
Scale-invariant principal component analysis (PCA) is prevalent in process monitoring because of its simplicity and efficiency. However, a number of limitations are associated with this technique because of underlying assumptions. This article attempts to relax these limitations by introducing three key elements. First, a semiparametric Gaussian transformation is proposed to make the process data follow a multivariate Gaussian distribution, such that the standard PCA can be directly applied to explain the majority of the process data variance. The Gaussian transformation function preserves both important statistical information and the correlation structures of the process data. Second, eigenvectors spanning the feature space are extracted using the Spearman correlation coefficient and the distance correlation coefficient. This feature space is able to retain nonlinear and nonmonotonic correlation structures of the process data. Finally, this technique is computationally more efficient than KPCA, KICA, and improved KICA by avoiding expensive kernel mapping. Semiparametric PCA is tested on two industrial case studies and exhibits satisfactory performance.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 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".