Cluster analysis with regression of non‐Gaussian functional data on covariates
Bibliographic record
Abstract
Cluster analysis with functional data often imposes normality assumptions on outcomes and is typically carried out without covariates or supervision. However, nonnormal functional data are frequently encountered in practice, and unsupervised learning, without directly tying covariates to clusters, often makes the resulting clusters less interpretable. To address these issues, we propose a new semiparametric transformation functional regression model, which enables us to cluster nonnormal functional data in the presence of covariates. Our model incorporates several unique features. First, it omits the normality assumptions on the functional response, which adds more flexibility to the modelling. Second, our model allows clusters to have distinct relationships between functional responses and covariates, and thus makes the clusters formed more interpretable. Third, unlike various competing methods, we allow the number of clusters to be unspecified and data‐driven. We develop a new method, which combines penalized likelihood and estimating equations, to estimate the number of clusters, regression parameters, and transformation functions simultaneously; we also establish the large‐sample properties such as consistency and asymptotic normality. Simulations confirm the utility of our proposed approach. We use our proposed method to analyze Chinese housing market data and garner some interesting findings.
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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 | 0.014 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".