Transcript Slide 1
MULTIPLE-SCALE PATTERN RECOGNITION: Application to Drought Prediction in Africa R Gil Pontius Jr ([email protected]) Hao Chen, and Olufunmilayo E Thontteh 1 Lessons • We present methods to compare two maps of a common real variable at multiple spatialresolutions. • 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. 2 How do these two maps compare? Map X Map Y 3 Map X at 16 fine resolution pixels -2 -1 7 8 -4 -3 5 6 -6 -5 3 4 -8 -7 1 2 4 Map Y at 16 fine resolution pixels 2 0 8 8 -2 0 6 6 -4 -4 2 6 -4 -2 -4 -2 5 Y versus X with west & east strata 6 Perfect Quantity Perfect Global Location 7 Posterior Quantity Perfect Global Location 8 Posterior Quantity Perfect In-Stratum Location 9 Posterior Quantity Posterior Location 10 Posterior Quantity Uniform In-Stratum Location 11 Posterior Quantity Uniform Global Location 12 Prior Quantity Uniform Global Location 13 Perfect Global Perfect In-Stratum Posterior Pixel Uniform In-Stratum INFORMATION OF LOCATION Uniform Global Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY 14 16 fine resolution pixels Xj 1 e 1 Xj 1 e 2 Xj 1 e 5 Xj 1 e 6 Xj 1 e 3 Xj 1 e 4 Xj 1 e 7 Xj 1 e 8 Xj 1 e 9 Xj 1 e 10 Xj 1 e 13 Xj 1 e 14 Xj 1 e 11 Xj 1 e 12 Xj 1 e 15 Xj 1 e 16 15 4 medium resolution pixels 4 Xj2e1 W 1en 8 Xj1en Xj2e2 n 1 4 W W Xj2e3 W 1en 8 W 1en 16 12 1en W 1en Xj2e4 n 9 n 9 1en n 5 Xj1en W Xj1en n 5 n 1 12 1en Xj1en n 13 16 W 1en n 13 16 1 coarse pixel 16 Xj4e1 W 1en Xj1en n 1 16 W 1en n 1 17 Perfect Global Perfect In-Stratum Posterior Pixel Uniform In-Stratum INFORMATION OF LOCATION Uniform Global Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY 18 Perfect Global Perfect In-Stratum Posterior Pixel Uniform In-Stratum INFORMATION OF LOCATION Uniform Global Components of Information for plots Perfect Posterior Prior INFORMATION OF QUANTITY 19 Uniform Global Uniform In-Stratum Wren Yje Xjren Posterior Pixel ˆ j Xjren Wren Y Wren Yjren E Nre e 1 n 1 E 2 Nre Nre E Nre e 1 n 1 2 Nre Wren e 1 n 1 E ~ Wren Yj Xjren E Wren e 1 n 1 2 e 1 n 1 E Nre Wren e 1 n 1 E Nre e 1 n 1 E Xjren 2 Nre Wren Perfect In-Stratum e 1 n 1 Nre n1 Wren Yjren Xjren Nre Wren n 1 2 E Nre Wren Yjren Xjren e 1 n 1 E Nre Wren e 1 n 1 2 Perfect Global INFORMATION OF LOCATION Components of Information for RMSE E e 1 0 Perfect Posterior Prior INFORMATION OF QUANTITY 20 Components of Information for MAE Wren Yˆ j Nre Xjren e 1 n 1 E Nre Uniform In-Stratum Posterior Pixel Wren Yjren Nre E Nre ~ Xjren e 1 n 1 Nre Wren e 1 n 1 E Wren Yj E Wren Wren Yje e 1 n 1 Xjren e 1 n 1 E Nre Wren e 1 n 1 E Nre Xjren e 1 n 1 E Nre Wren Perfect In-Stratum e 1 n 1 Nre E Wren Yjren Xjren n 1 Nre Wren e 1 n 1 E Perfect Global INFORMATION OF LOCATION Uniform Global E 0 Perfect Nre Wren Yjren Xjren e 1 n 1 E Nre Wren e 1 n 1 Posterior Prior INFORMATION OF QUANTITY 21 Component Budgets for RMSE and MAE 8 8 Agreement due to Posterior Quantity Agreement due to Stratum-level Location Agreement due to Pixellevel Location Disagreement due to Pixel-level Location Disagreement due to Stratum-level Location Disagreement due to Posterior Quantity 6 5 4 3 2 1 7 Mean Absolute Error Root Mean Square Error 7 Agreement due to Posterior Quantity Agreement due to Stratum-level Location Agreement due to Pixellevel Location Disagreement due to Pixel-level Location Disagreement due to Stratum-level Location Disagreement due to Posterior Quantity 6 5 4 3 2 1 0 0 fine medium coarse all fine medium coarse all 22 NDVI deviation at 8X8 km Truth versus Predicted Null model predicts zero everywhere. 23 NDVI deviation at 32X32 km Truth versus Predicted Null model predicts zero everywhere. 24 NDVI deviation at 128X128 km Truth versus Predicted Null model predicts zero everywhere. 25 NDVI deviation Regression at 8X8 km Red Line is Y=X, Black Line is Least Squares (-0.7,0.0) (-0.5,-0.7) -1.6 -0.7 (0.0,-0.7) +0.2 26 Regression at resolution multiples: 1, 2, 4, & 8 27 Regression at resolution multiples: 16, 32, 64, & 128 28 3 Upper Confidence Bound for Slope 2 1 Slope of Least Squares Line 0 -1 Lower Confidence Bound for Slope -2 128 64 32 16 8 4 2 -3 1 Coefficient of Linear Association Confidence Intervals for Slope Resolution as multiple of fine pixel side 29 Prediction versus Null 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 Root Mean Square Error 0.3 0.2 0.1 256 128 64 32 16 8 4 2 1 128 64 32 16 8 4 2 1 256 Resolution as multiple of fine pixel side Resolution as multiple of fine pixel side 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 0.0 Mean Absolute Error 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 Resolution as multiple of fine pixel side 256 128 64 32 16 8 4 256 128 64 32 16 8 4 2 1 0.0 2 Mean Absolute Error Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.0 0.0 • 0.5 1 Root Mean Square Error 0.6 Resolution as multiple of fine pixel side 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. 30 Interpretation of RMSE 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 256 128 64 32 16 8 4 2 1 256 128 64 32 16 8 4 2 1 Resolution as multiple of fine pixel side • • 0.5 0.0 0.0 • Root Mean Square Error Root Mean Square Error 0.6 Resolution as multiple of fine pixel side 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. 31 Interpretation of MAE 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 0.0 Mean Absolute Error 0.6 0.5 Agreement due to Location Disagreement due to Location Disagreement due to Quantity 0.4 0.3 0.2 0.1 Resolution as multiple of fine pixel side 256 128 64 32 16 8 4 2 1 256 128 64 32 16 8 4 2 0.0 1 • 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. Mean Absolute Error • Resolution as multiple of fine pixel side 32 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. 33 Lessons • We present methods to compare two maps of a common real variable at multiple spatialresolutions. • 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. 34 Plugs & Acknowledgements 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 [email protected] 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 35