MULTIPLE-SCALE PATTERN RECOGNITION: Application to Drought Prediction in Africa

MULTIPLE-SCALE PATTERN RECOGNITION:Application to Drought Prediction in Africa

R Gil Pontius Jr (rpontius@clarku.edu)

Hao Chen, and Olufunmilayo E

Thontteh

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.

How do these two maps compare?

Map YMap X

Map X at 16 fine resolution pixels

-6 -5 3 4

-8 -7 1

Map Y at 16 fine resolution pixels

-4 -4 2 6

-4 -2 -4

Y versus X with west & east strata

Perfect QuantityPerfect Global Location

Posterior QuantityPerfect Global Location

Posterior QuantityPerfect In-Stratum Location

Posterior QuantityPosterior Location

Posterior QuantityUniform In-Stratum Location

Posterior QuantityUniform Global Location

Prior QuantityUniform Global Location

Components of Information for plots

Perfect Posterior PriorINFORMATION OF QUANTITY

16 fine resolution pixels

Xj 1 e 4

Xj 1 e 1 Xj 1 e 2

Xj 1 e 16

Xj 1 e 3

Xj 1 e 5 Xj 1 e 6

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

4 medium resolution pixels

j1en1en

1 coarse pixel

j1en1en

Components of Information for RMSE

Wren XjrenjY~

XjrenYjrenWren

Wren XjrenYjren

Wren XjrenjeY

Wren XjrenjY

XjrenYjrenWren2

Components of Information for MAE

XjrenjY~

XjrenYjrenWren

XjrenjeYWren

XjrenjYWren

Component Budgets forRMSE and MAE

fine medium coarse all

Agreement due toPosterior Quantity

Agreement due toStratum-level Location

Agreement due to Pixel-level Location

Disagreement due toPixel-level Location

Disagreement due toStratum-level Location

Disagreement due toPosterior Quantity

fine medium coarse allM

Agreement due toPosterior Quantity

Agreement due toStratum-level Location

Agreement due to Pixel-level Location

Disagreement due toPixel-level Location

Disagreement due toStratum-level Location

Disagreement due toPosterior Quantity

NDVI deviation at 8X8 km Truth versus Predicted

Null model predicts zero everywhere.

NDVI deviation Regression at 8X8 kmRed 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)

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

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

Confidence Intervals for Slope

31 2 4 8

Resolution as multiple of fine pixel side

UpperConfidenceBound for Slope

Slope of LeastSquares Line

LowerConfidenceBound for Slope

Prediction versus Null

1 2 4 8

Agreement due toLocation

Disagreement due toLocation

Disagreement due toQuantity

1 2 4 8

• 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.

Interpretation of RMSE

1 2 4 8

• 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.

Interpretation of MAE

1 2 4 8

• 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.

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.

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.

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 ChangeHuman Environment Regional Observatory (HERO)

We extent special thanks to: Clarklabs (www.clarklabs.org) who is incorporating this into the GIS software IdrisiRon Eastman who supplied dataGeorge Kariuki who helped with analysis

Plugs & Acknowledgements

MULTIPLE-SCALE PATTERN RECOGNITION: Application to Drought Prediction in Africa

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