A Robust Nonparametric Framework for Detecting Repeated Spatial Patterns
Bibliographic record
Abstract
Identifying spatially contiguous clusters and repeated spatial patterns (RSP) characterized by similar underlying distributions that are spatially apart is a key challenge in modern spatial statistics. Existing constrained clustering methods enforce spatial contiguity but are limited in their ability to identify RSP. We propose a novel nonparametric framework that addresses this limitation by combining constrained clustering with a post-clustering reassigment step based on the maximum mean discrepancy (MMD) statistic. We employ a block permutation strategy within each cluster that preserves local attribute structure when approximating the null distribution of the MMD. We also show that the MMD 2 statistic is asymptotically consistent under model-free spatial mixing conditions. This two-stage approach enables the detection of clusters that are both spatially distant and similar in distribution. Through simulation studies that vary spatial dependence, cluster sizes, shapes, and multivariate dimensionality, we demonstrate the robustness of our proposed framework in detecting RSP. We further illustrate its applicability through an analysis of spatial proteomics data from patients with triple-negative breast cancer. Overall, our framework presents a methodological advancement in spatial clustering, offering a flexible and robust solution for spatial datasets that exhibit repeated patterns.
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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 | 0.008 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| 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".