1. 1 MULTIPLE-SCALE PATTERN RECOGNITION: Application to Drought Prediction in Africa R Gil Pontius Jr (rpontius@clarku.edu)rpontius@clarku.edu Hao Chen, and Olufunmilayo E Thontteh

2. 2 Lessons We present methods to compare two maps of a common real variable at multiple spatial- resolutions. We examine various components of two measures of accuracy: –Root Mean Square Error (RMSE) –Mean Absolute Error (MAE) The proposed methods are better than regression at giving useful information to evaluate prediction of drought in Africa.

3. 3 How do these two maps compare? Map Y Map X

4. 4 Map X at 16 fine resolution pixels -3 -2 2 -4 78 56 -6-534 -8-71

5. 5 Map Y at 16 fine resolution pixels 0 20 -2 88 66 -4 26 -2-4

6. 6 Y versus X with west & east strata

7. 7 Perfect Quantity Perfect Global Location

8. 8 Posterior Quantity Perfect Global Location

9. 9 Posterior Quantity Perfect In-Stratum Location

10. 10 Posterior Quantity Posterior Location

11. 11 Posterior Quantity Uniform In-Stratum Location

12. 12 Posterior Quantity Uniform Global Location

13. 13 Prior Quantity Uniform Global Location

14. 14 Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

15. 15 16 fine resolution pixels X j 1 e 4 X j 1 e 1 X j 1 e 2 X j 1 e 16 X j 1 e 3 X j 1 e 5 X j 1 e 6 X j 1 e 7 X j 1 e 8 X j 1 e 9 X j 1 e 10 X j 1 e 13 X j 1 e 14 X j 1 e 11 X j 1 e 12 X j 1 e 15

16. 16 4 medium resolution pixels

17. 17 1 coarse pixel

18. 18 Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

19. 19 Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

20. 20 Components of Information for RMSE Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

21. 21 Components of Information for MAE Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

22. 22 Component Budgets for RMSE and MAE

23. 23 NDVI deviation at 8X8 km Truth versus Predicted Null model predicts zero everywhere.

24. 24 NDVI deviation at 32X32 km Truth versus Predicted Null model predicts zero everywhere.

25. 25 NDVI deviation at 128X128 km Truth versus Predicted Null model predicts zero everywhere.

26. 26 NDVI deviation Regression at 8X8 km Red Line is Y=X, Black Line is Least Squares -1.6+0.2-0.7 (0.0,-0.7) (-0.7,0.0) (-0.5,-0.7)

27. 27 Regression at resolution multiples: 1, 2, 4, & 8

28. 28 Regression at resolution multiples: 16, 32, 64, & 128

29. 29 Confidence Intervals for Slope

30. 30 Prediction versus Null Disagreement of quantity shows the model predicted accurately that it would be a low year, and predicted that it would be lower than it actually was.

31. 31 Interpretation of RMSE At all resolutions, the model prediction would be more accurate if it were to assign the average of -0.7 to each pixel. At resolutions at or finer than 4, the Null model is better than the prediction. At resolutions coarser than 4, the prediction is better than the Null model.

32. 32 Interpretation of MAE At all resolutions, the model prediction would be more accurate if it were to assign the average of -0.7 to each pixel. At all resolutions, the prediction is better than a Null model, because the prediction’s quantity better than a Null model.

33. 33 RMSE versus MAE Only perfect spatial arrangement minimizes RMSE, whereas many spatial arrangements can minimize MAE. RMSE gives larger penalty than MAE for outliers, thus RMSE is more sensitive to changes in resolution. MAE is consistent with the categorical variable case.

34. 34 Lessons We present methods to compare two maps of a common real variable at multiple spatial- resolutions. We examine various components of two measures of accuracy: –Root Mean Square Error (RMSE) –Mean Absolute Error (MAE) The proposed methods are better than regression at giving useful information to evaluate prediction of drought in Africa.

35. 35 Method is based on: Pontius. 2002. Statistical methods to partition effects of quantity and location during comparison of categorical maps at multiple resolutions. Photogrammetric Engineering & Remote Sensing 68(10). pp. 1041-1049. PDF file is available at www.clarku.edu/~rpontius or rpontius@clarku.edu National Science Foundation funded this via: Center for Integrated Study of the Human Dimensions of Global Change Human Environment Regional Observatory (HERO) We extent special thanks to: Clarklabs (www.clarklabs.org) who is incorporating this into the GIS software Idrisi Ron Eastman who supplied data George Kariuki who helped with analysis Plugs & Acknowledgements