Geographically Weighted Regression Effects on Soil Zinc Content Hyperspectral Modeling by Applying the Fractional-Order Differential
Bibliographic record
Abstract
With the development of remote sensing techniques and the increasing need for soil contamination monitoring, we estimated soil heavy metal zinc (Zn) content using hyperspectral imaging. Geographically weighted regression (GWR), an extension of the ordinary least squares (OLS) regression framework, was proposed. By estimating a set of parameters for any number of locations in a study area, GWR can probe the spatial heterogeneity in data relationships, whereas the regression parameters of an OLS model are global and aspatially-varied. The objectives of this study were: (1) To find the possible relationships between hyperspectral data and soil Zn content, and (2) to investigate the existence of their spatial heterogeneity. In this study, 67 soil samples collected from Pingtan Island, Fujian Province, China, were used to conduct laboratory hyperspectral modeling for soil Zn content estimation. Four transformations of square root, logarithm, reciprocal of logarithm, and reciprocal, as well as the fractional-order differential operations were applied to increase the amount of reflectance data in which the effective variables for modeling might be involved, and to enhance the spectral characteristics of soil Zn content. To find sensitive variables and to remove redundancy and multicollinearity in the spectra, a data sifting process was applied by selecting wavelengths with local maximum in the absolute values of the correlation coefficients with Zn content in one type of spectral data and by employing Variance Inflation Factors. Since a modeling sample size of 46 is insufficient to construct the appropriate OLS and GWR models, four methods are proposed using all 67 samples to choose explanatory variables. A random process to select 57 samples for modeling and 10 samples for validation was applied to assess model performance, in which the mean verification R2 (Rv2) was used as an indicator. The results show that GWR stepwise regression is the most effective method to select better variables. As the mean Rv2 converges toward the OLS value when the bandwidth of the GWR model increases, the four variables selected by the GWR stepwise regression were used to establish the representative OLS and GWR models. The representative OLS model has the best mean verification effect among all studied models, which had a mean Rv2 value that is 44.6% higher than the OLS model constructed using OLS stepwise regression.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".