A variational method to determine the most representative shape of a set of curves and its application to knee kinematic data for pathology classification
Bibliographic record
Abstract
The purpose of this study is to investigate a variational method to determine the most representative shape of a family of curves and its application to three-dimensional knee kinematic data for knee pathology classification. High variability and the presence of outliers are characteristic of the data in this application. This method determines the most representative shape by averaging the family curves corrected to account for outliers occurrence and family variability. To this effect, the correction is performed by simultaneous minimization of a set of objective functions, one for each family curve consisting of two terms: a data term of conformity of the corrected curve to the given family curve, and a regularization term of proximity of the corrected curve to the mean of the corrected curves to inhibit the influence of outliers in the family. Minimization is carried out efficiently by particle swarm optimization, a method which, in contrast to gradient descent, is robust to the presence of outliers. Experimental results using real-world data in knee osteoarthritis pattern classification demonstrate the validity and efficiency of the method. Comparisons to conventional methods used to determine the most representative shape are given.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".