multiple-scale pattern recognition: application to drought prediction in africa

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

R Gil Pontius Jr ([email protected])

Hao Chen, and Olufunmilayo E

Thontteh

mailto:[email protected]

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.

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How do these two maps compare?

Map YMap X

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Map X at 16 fine resolution pixels

-3

-2 -1

2

-4

7 8

5 6

-6 -5 3 4

-8 -7 1

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Map Y at 16 fine resolution pixels

0

2 0

-2

-2

8 8

6 6

-4 -4 2 6

-4 -2 -4

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Y versus X with west & east strata

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Perfect QuantityPerfect Global Location

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Posterior QuantityPerfect Global Location

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Posterior QuantityPerfect In-Stratum Location

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Posterior QuantityPosterior Location

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Posterior QuantityUniform In-Stratum Location

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Posterior QuantityUniform Global Location

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Prior QuantityUniform Global Location

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Components of Information for plots

Perfect Posterior PriorINFORMATION OF QUANTITY

Pe

rfe

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ect

Po

ste

rior

Un

iform

Un

iform

Glo

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mG

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INF

OR

MA

TIO

N O

F L

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AT

ION

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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

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4 medium resolution pixels

4

1n

1en

4

1n

j1en1en

j2e1

W

XWX

12

9n

1en

12

9n

j1en1en

j2e3

W

XWX

8

5n

1en

8

5n

j1en1en

j2e2

W

XWX

16

13n

1en

16

13n

j1en1en

j2e4

W

XWX

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1 coarse pixel

16

1n

1en

16

1n

j1en1en

j4e1

W

XWX

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Pe

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ect

Po

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rior

Un

iform

Un

iform

Glo

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-Str

atu

mP

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lIn

-Str

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mG

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INF

OR

MA

TIO

N O

F L

OC

AT

ION

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Pe

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ect

Po

ste

rior

Un

iform

Un

iform

Glo

ba

lIn

-Str

atu

mP

ixe

lIn

-Str

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mG

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INF

OR

MA

TIO

N O

F L

OC

AT

ION

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Components of Information for RMSE


Pe

rfe

ctP

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ect

Po

ste

rior

Un

iform

Un

iform

Glo

ba

lIn

-Str

atu

mP

ixe

lIn

-Str

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mG

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al

INF

OR

MA

TIO

N O

F L

OC

AT

ION

0

E

1e

Nre

1n

E

1e

Nre

1n

2

Wren

Wren XjrenjY~

E

1e

2

Nre

1n

Nre

1n

Wren

XjrenYjrenWren

E

1e

Nre

1n

E

1e

Nre

1n

2

Wren

Wren XjrenYjren

E

1e

Nre

1n

E

1e

Nre

1n

2

Wren

Wren XjrenjeY

E

1e

Nre

1n

E

1e

Nre

1n

2

Wren

Wren XjrenjY

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenYjrenWren2

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Components of Information for MAE


Pe

rfe

ctP

erf

ect

Po

ste

rior

Un

iform

Un

iform

Glo

ba

lIn

-Str

atu

mP

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lIn

-Str

atu

mG

lob

al

INF

OR

MA

TIO

N O

F L

OC

AT

ION

0

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenjY~

Wren

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenYjrenWren

E

1eNre

1n

Nre

1n

Wren

XjrenYjrenWren

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenYjrenWren

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenjeYWren

E

1e

Nre

1n

E

1e

Nre

1n

Wren

XjrenjYWren

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Component Budgets forRMSE and MAE

0

1

2

3

4

5

6

7

8

fine medium coarse all

Roo

t Mea

n S

quar

e E

rror

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

0

1

2

3

4

5

6

7

8

fine medium coarse allM

ean

Abs

olut

e E

rror

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

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NDVI deviation at 8X8 km Truth versus Predicted

Null model predicts zero everywhere.

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25



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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)

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

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

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Confidence Intervals for Slope

-3

-2

-1

0

1

2

31 2 4 8

16

32

64

12

8

Resolution as multiple of fine pixel side

Co

eff

icie

nt

of

Lin

ea

r A

ss

oc

iati

on

UpperConfidenceBound for Slope

Slope of LeastSquares Line

LowerConfidenceBound for Slope

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Prediction versus Null

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 4 8

16

32

64

12

8

25

6


Ro

ot

Me

an

Sq

ua

re E

rro

r

Agreement due toLocation

Disagreement due toLocation

Disagreement due toQuantity

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 4 8

16

32

64

12

8

25

6


Ro

ot

Me

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Sq

ua

re E

rro

r




0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 4 8

16

32

64

12

8

25

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Me

an

Ab

so

lute

Err

or




0.0

0.1

0.2

0.3

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1 2 4 8

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• 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.

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Interpretation of RMSE

0.0

0.1

0.2

0.3

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0.5

0.6

1 2 4 8

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0.0

0.1

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• 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.

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Interpretation of MAE

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 4 8

16

32

64

12

8

25

6


Me

an

Ab

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lute

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or




0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 4 8

16

32

64

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Me

an

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• 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.

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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.

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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.

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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 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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