Spatial Classification and Prediction

1. Spatial Classification and Prediction Zhe Jiang zjiang@cs.ua.edu

2. Applications Earth image classification (wetland mapping) Prediction of Soil Property (usda.gov) Disease risk mapping (http://lab.mappler.net/)

3. Problem Definition: Basic Concept • Spatial raster framework • A tessellation of 2D plane into a grid • Multiple feature layers, a class layer • Spatial data sample • A pixel or location • , is feature vector, is location, is class • Training samples: is known • Test samples: hidden • Spatial neighborhood relationship • Range of spatial dependency • Adjacency matrix , when are neighbors

4. Problem Definition • Given: • Training and test samples from a raster framework • Spatial neighborhood relationship • Find: • A classification model: (spatial) decision tree • Objective: • Minimize classification error • Constraint: • Spatial autocorrelation exists in class map (pixel size << class parcel) • Large training set consists of contiguous patches

5. Problem Example Aerial photo (NIR,G,B) in spring (b) Aerial photo (R,G,B) in summer (c) Ground truth wetland map (d) Decision tree prediction Wetland Dry land Analysis of prediction results • Salt-and-pepper noisein decision tree prediction • Require labor intensive pre/post-processing • General issue for many models: random forest, SVM, neural network.

6. Problem Example: Traditional Decision Tree Input: Output: Decision Tree f1 ≤ 1 no yes Feature map f1 Feature map f2 Pixel ID and classes green red A M D P Table columns: 1. Features f1, f2 2. Classes: red, green Table rows: Spatial data samples N E Q B F R C O K J H G L I Predicted map Salt-and-pepper noise H and K 3 by 3 neighborhood

7. Challenges • Autocorrelation effect • Tobler’sfirst law of geography • Violates assumption of identical and independent distribution (i.i.d.) • Salt-and-pepper noise • Anisotropy • Spatial dependency varies across directions • Asymmetric spatial neighborhood • Computational cost • Computation with spatial neighborhoods of different sizes Ground truth classes Decision tree prediction

8. Potential Solutions • Spatial features • Median filter • Spatial contextual variable (texture) • Focal tree node test • Modify greedy heuristic • Spatial entropy or information gain

9. Potential Solution 1: Spatial Features • Median filter Feature map f1 Feature map f2 Pixel ID and classes Feature map f1 Feature map f2 Pixel ID and classes Decision tree prediction Pros: simple methods to remove salt-and-pepper noise in feature maps Cons: need to choose good window size; “over-smoothing” effect; not good at salt-and-pepper noise errors due to textures

10. Potential Solution 1: Spatial Features • Spatial contextual variables (textures) • Draw a square window W of size d • Compute homogeneity/heterogeneity of values in W • Often generate features from multiple window sizes Wetland Dry land Aerial photo (NIR,G,B) in spring (b) Aerial photo (R,G,B) in summer (c) Ground truth wetland map (d) Decision tree prediction Pro: prediction based on not only single pixel value, but also spatial context Con: computationally expensive, may generate features that are not used

11. Potential Solution 2: Focal Tree Node Test (a) Feature f (b) Focal function Γ (c) Local indicator I(f ≤ 1) (d) Focal test I XΓ I(f ≤ 1) I X Γ + - + - green red green red Local Focal Zonal Global (e) Local tree (f) Focal tree Over-simplified example with rook neighborhood (g) Local prediction (h) Focal prediction

12. Focal Tree Node Test: Illustrative Example Traditional decision tree Spatial decision tree • Inputs: • Feature maps, class map • Rook (four) neighborhood Inputs: table of records Feature f1 I(f1 ≤ 1) I(f1≤ 1) * Γ1 - - + + green red green red A M D P A M D P Feature f2 E B Q N E B Q N O F R C O F R C H K J G K H J G L L I I Class map Focal function Γ1 Predicted map Predicted map

13. Focal Tree Node Test: Adaptive Spatial Neighborhoods • Why adaptive spatial neighborhoods? • Rich texture in high resolution feature images • Fixed neighborhoods cause over-smoothing effect • How to form adaptive spatial neighborhood? • Create local indicator map I(f ≤ δ) within window (Smaxby Smax) • Identify connected components of same indicator • The outmost component surrounding current pixel Example: True class map Focal test results and predictions Local test (numbers), adaptive neighborhood(blue) Local feature test, fixed neighborhood (blue) Focal test results and predictions

14. Focal Tree Node Test: Computational Refinement • Key idea • Focal value maps don’t change a lot for different thresholds • Gradually increase candidate test threshold • Incrementally update local and focal results • Illustrative example (a) Feature values (b) Indicators, focal values, δ=1 (c) Indicators, focal values. δ=2 Candidate threshold δ: {1, 2, 3, 4, 5, 6, 7, 8} Queen (3 by 3) neighborhood. (d) Indicators, focal values, δ=3 (intermediate) (e) Indicators, focal values, δ=3 (final) Saved computation New computation

15. Potential Solution 3: Spatial Information Gain • Input: two feature maps, land cover type map Feature 2 without noise Feature 1 with noise

16. Spatial Information Gain (SIG) Feature 1: best Split Feature 1: best Split Feature 1 with noise Entropy is same both. Before split: 34 blue, 30 red After split: 26 blue 4 red 8 blue 26 red Bad choice Feature 2: best split Feature 2: best split Feature 2 without noise Good choice

17. Spatial Information Gain (SIG) • Neighborhood split autocorrelation ratio • if and are neighbors, otherwise • if and are split into same subset, otherwise • In previous example: • is same for feature 1 and feature 2; however, is bigger for feature 2 • Feature 2 will be selected • Will this method always work? • If all features are bad (poor spatial autocorrelation ) • Still have to select one, does not change feature or test

18. Some Evaluation Results Spatial decision tree (fixed) Spatial decision tree (adaptive) Decision tree True wetland True dry land False dry land False wetland Analysis of results: DT: salt-and-pepper noise SDT improve accuracy, salt-and-pepper noise levels SDT with adaptive neighborhoods best accuracy

19. Summary • Three approaches to enhance decision trees for spatial classification • Spatial features • Spatial tree node test formula • Spatial greedy heuristic • Focal-test in tree nodes is effective, but additional challenges remain

20. References: [1]: Jiang Z, Shekhar S, Zhou X, Knight J, Corcoran J. Focal-test-based spatial decision tree learning. IEEE Transactions on Knowledge and Data Engineering. 2015 Jun 1;27(6):1547-59. [2]: Jiang Z, Shekhar S, Mohan P, Knight J, Corcoran J. Learning spatial decision tree for geographical classification: a summary of results. InProceedings of the 20th International Conference on Advances in Geographic Information Systems 2012 Nov 6 (pp. 390-393). ACM.