Development of a Python package for Functional Data Analysis. Depth measures, applications and clustering
Bibliographic record
Abstract
In this paper, the problem of analyzing functional data is addressed. Each observation in functional data is a function that varies over a continuum. This kind of complex data is increasingly becoming more common in many research fields. However, Functional Data Analysis (FDA) is a relatively recent field in which software implementations are basically limited to R. In addition, although they may follow an open-source scheme, the contribution to them may turn out to be complicated. The final goal of this project is to provide a comprehensive Python package for Functional Data Analysis, scikit-fda. In this undergraduate thesis, the functionality implemented in the package includes functional depth measures together with their applications and elementary notions of clustering. In a functional space, establishing an order is complicated due to its nature. Depth measures allow to define robust statistics for functional data. In the package you can find some of the most common, Fraiman and Muniz depth measure, the band depth measure or a modification of the latter, the modified band depth. Depth measures are used in the construction of graphic tools, both the functional boxplot and the magnitude-shape plot are introduced in the package along with their outlier detection procedures. Furthermore, contributions in the area of machine learning are made in which basic clustering algorithms are added to the package: K-means and Fuzzy K-means. Finally, the results of applying these methods to the Canadian Weather dataset are shown. The Python package is published in a GitHub repository. It is open-source wth the aim of growing and being kept up to date. In the long term it is expected to cover the fundamental techniques in FDA and become a widely-used toolbox for research in FDA.
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.080 | 0.066 |
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".