Linear Regression
Fits a straight-line relationship between one raster band and the target.
ŷ = β0 + β1x
Best used when: one predictor has an approximately linear relationship with the target.
Raster Modeller
Build a raster prediction model from training points with a numeric target field, then predict that continuous variable across the predictor raster.
Remote Sensing CoreEnd-User DocumentationTheory + Formula + Parameters1. What This Feature Does
Build a raster prediction model from training points with a numeric target field, then predict that continuous variable across the predictor raster.
Cloud workflow: choose data → configure the scientific method → run → review the resulting layer/report. No programming is required.
2. Recommended Workflow
Prepare predictor bands and training points.
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Select the numeric target field.
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Choose a regression method.
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Configure model complexity and training controls.
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Train and predict the continuous output raster.
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Validate using independent samples whenever possible.
3. Theory, Methods & Equations
Multiple Linear Regression
Extends linear regression to multiple bands/features.
ŷ = β0 + Σj=1..pβjxj
Best used when: several predictors have a roughly linear additive relationship.
Random Forest Regression
Averages predictions from many decision trees trained on randomized samples/features.
ŷ(x)= (1/T)Σt=1..T ft(x)
Best used when: relationships are nonlinear and interactions matter.
SVM / SVR Regression
Fits a function with an ε-insensitive error tube and kernel-based nonlinear mapping.
min ½||w||² + CΣ(ξi+ξi*)
|yi−f(xi)| ≤ ε + ξ
Best used when: sample size is moderate and nonlinear regression is needed.
ANN Regression
Learns nonlinear transformations through stacked neural layers.
h(l)=φ(W(l)h(l−1)+b(l))
MSE=(1/n)Σ(y−ŷ)²
Best used when: enough representative training samples exist for neural regression.
KAN Regression
Uses learnable univariate spline-like functions on network edges following the Kolmogorov–Arnold representation concept.
f(x) ≈ Σq Φq(Σp φqp(xp))
Best used when: flexible nonlinear relationships are needed and KAN experimentation is appropriate.
Transformer Regression
Treats predictor bands/features as a sequence of tokens/features and learns attention-weighted interactions.
Attention(Q,K,V)=softmax(QKT/√dk)V
Best used when: cross-band interactions are complex and sufficient training data/computation are available.
4. Input Data
| Input | Type | Requirement | Description |
|---|---|---|---|
| Predictor raster | raster | Required | |
| Training points | vector | Required |
5. Parameters Available in the Application
| Parameter | Default | Choices / Range | How to Use It |
|---|---|---|---|
| Algorithm | — | Linear Regression (single band), Multiple Linear Regression (multi-band), Random Forest Regression, SVM / SVR Regression, ANN Regression, KAN Regression (Kolmogorov-Arnold Network), Transformer Regression | Select a model first so only its relevant inputs and parameters are displayed. |
| Target field | — | — | Numeric field from the training-point layer to be predicted. Shown for: linear_regression, multiple_linear_regression, random_forest, svm, ann, kan, transformer |
| Predictor band | 1 | 1 to — | Linear Regression uses exactly one predictor band. Shown for: linear_regression |
| Select Input Bands | — | — | Band numbers, for example [1,2,3]. Default is All bands. Select specific bands only when needed. MLR and Transformer require at least two bands. Shown for: multiple_linear_regression, random_forest, svm, ann, kan, transformer |
| RF trees | 300 | 10 to 2000 | Shown for: random_forest |
| RF max depth | — | 1 to 100 | Leave empty for no explicit maximum depth. Shown for: random_forest |
| SVM kernel | rbf | rbf, linear, poly, sigmoid | Shown for: svm |
| SVM C | 1.0 | 1e-06 to — | Shown for: svm |
| SVM gamma | scale | — | Use scale, auto, or a positive numeric value. Shown for: svm |
| SVM epsilon | 0.1 | 0.0 to — | Shown for: svm |
| ANN hidden layers | [64, 32] | — | Shown for: ann |
| ANN max iteration | 500 | 10 to 10000 | Shown for: ann |
| KAN hidden layers | [16, 8] | — | KAN hidden-layer widths, for example [16,8]. Shown for: kan |
| KAN grid size | 5 | 2 to 32 | Number of spline-grid intervals per edge. Shown for: kan |
| KAN spline order | 3 | 1 to 5 | Shown for: kan |
| KAN epochs | 200 | 10 to 10000 | Shown for: kan |
| KAN learning rate | 0.01 | 1e-06 to 1.0 | Shown for: kan |
| KAN batch size | 1024 | 8 to 65536 | Shown for: kan |
| KAN weight decay | 0.0 | 0.0 to — | Shown for: kan |
| KAN device | auto | auto, cpu, cuda | auto uses CUDA when available, otherwise CPU. Shown for: kan |
| Transformer embedding size (d_model) | 64 | 4 to 1024 | Embedding width used by the Transformer encoder. It must be divisible by the attention-head count. Shown for: transformer |
| Transformer attention heads | 4 | 1 to 32 | Shown for: transformer |
| Transformer encoder layers | 2 | 1 to 12 | Shown for: transformer |
| Transformer feed-forward size | 128 | 4 to 8192 | Shown for: transformer |
| Transformer dropout | 0.1 | 0.0 to 0.9 | Shown for: transformer |
| Transformer epochs | 200 | 10 to 10000 | Shown for: transformer |
| Transformer learning rate | 0.001 | 1e-06 to 1.0 | Shown for: transformer |
| Transformer batch size | 512 | 8 to 65536 | Shown for: transformer |
| Transformer weight decay | 1e-05 | 0.0 to — | Shown for: transformer |
| Transformer device | auto | auto, cpu, cuda | auto uses CUDA when available, otherwise CPU. Shown for: transformer |
| Random state | 42 | — | Shown for: random_forest, ann, kan, transformer |
| Output nodata | -9999 | — | Shown for: linear_regression, multiple_linear_regression, random_forest, svm, ann, kan, transformer |
6. Output & Interpretation
The result should be interpreted according to the selected method and the physical meaning of the input data. Preserve source units, coordinate reference information, NoData meaning, acquisition date, and preprocessing level when comparing results.
Scientific interpretation: an algorithm can produce a numerically valid result even when the input data are unsuitable. Always check masks, units, sensor characteristics, spatial resolution and reference data.
7. Best Practices
- Use analysis-ready inputs and remove invalid/cloud/noise artifacts that are not part of the target phenomenon.
- Choose parameters from the physical scale of the data, not only from visual appearance.
- Keep categorical and continuous rasters conceptually separate when selecting interpolation/resampling methods.
- Compare the result with the source image and independent reference information.
- Document the settings used when results will be compared across dates, sensors or study areas.