Post on 03-Jan-2016
description
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MULTIPLE-SCALE PATTERN RECOGNITION:Application to Drought Prediction in Africa
R Gil Pontius Jr (rpontius@clarku.edu)
Hao Chen, and Olufunmilayo E
Thontteh
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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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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
5
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
8
Posterior QuantityPerfect Global Location
9
Posterior QuantityPerfect In-Stratum Location
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Posterior QuantityPosterior Location
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Posterior QuantityUniform In-Stratum Location
12
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
ctP
erf
ect
Po
ste
rior
Un
iform
Un
iform
Glo
ba
lIn
-Str
atu
mP
ixe
lIn
-Str
atu
mG
lob
al
INF
OR
MA
TIO
N O
F L
OC
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
16
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
17
1 coarse pixel
16
1n
1en
16
1n
j1en1en
j4e1
W
XWX
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Components of Information for plots
Perfect Posterior PriorINFORMATION OF QUANTITY
Pe
rfe
ctP
erf
ect
Po
ste
rior
Un
iform
Un
iform
Glo
ba
lIn
-Str
atu
mP
ixe
lIn
-Str
atu
mG
lob
al
INF
OR
MA
TIO
N O
F L
OC
AT
ION
19
Components of Information for plots
Perfect Posterior PriorINFORMATION OF QUANTITY
Pe
rfe
ctP
erf
ect
Po
ste
rior
Un
iform
Un
iform
Glo
ba
lIn
-Str
atu
mP
ixe
lIn
-Str
atu
mG
lob
al
INF
OR
MA
TIO
N O
F L
OC
AT
ION
20
Components of Information for RMSE
Perfect Posterior PriorINFORMATION OF QUANTITY
Pe
rfe
ctP
erf
ect
Po
ste
rior
Un
iform
Un
iform
Glo
ba
lIn
-Str
atu
mP
ixe
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
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
Perfect Posterior PriorINFORMATION OF QUANTITY
Pe
rfe
ctP
erf
ect
Po
ste
rior
Un
iform
Un
iform
Glo
ba
lIn
-Str
atu
mP
ixe
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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NDVI deviation at 32X32 km Truth versus Predicted
Null model predicts zero everywhere.
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NDVI deviation at 128X128 km Truth versus Predicted
Null model predicts zero everywhere.
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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
Resolution as multiple of fine pixel side
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
Resolution as multiple of fine pixel side
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
Resolution as multiple of fine pixel side
Me
an
Ab
so
lute
Err
or
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
Resolution as multiple of fine pixel side
Me
an
Ab
so
lute
Err
or
Agreement due toLocation
Disagreement due toLocation
Disagreement due toQuantity
• 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
0.4
0.5
0.6
1 2 4 8
16
32
64
12
8
25
6
Resolution as multiple of fine pixel side
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
Resolution as multiple of fine pixel side
Ro
ot
Me
an
Sq
ua
re E
rro
r
Agreement due toLocation
Disagreement due toLocation
Disagreement due toQuantity
• 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
Resolution as multiple of fine pixel side
Me
an
Ab
so
lute
Err
or
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
Resolution as multiple of fine pixel side
Me
an
Ab
so
lute
Err
or
Agreement due toLocation
Disagreement due toLocation
Disagreement due toQuantity
• 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 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