Implementing kohonen's som with missing data in OTB

Implementing Kohonen’s SOM withMissing Data in OTBGregoire Mercier and Bassam Abdel LatifInstitut Telecom; Telecom BretagneCNRS UMR 3192 lab-STICC, team CIDTechnopole Brest-Iroise,CS 83818, F-29238 Brest Cedex 3, FranceIGARSS, 2009

The Kohonen MapClouds and Shadows in times series

Benefits in Generic Programming

PropertiesDescription

Contents

1 The Kohonen MapPropertiesDescription

2 Clouds and Shadows in times seriesModification to deal with missing valueModification to deal with erroneous value

3 Benefits in Generic Programming

page 2 G Mercier & B Abdel Latif Kohonen map in the OTB




The Kohonen Map

Properties

� Neural network of 1 fully connected layer to be trained by supervized orunsupervized approaches

� Corresponds to a transformation Rn =⇒ R, R2 or R3

• Visualization• Compression

� Neurons in their neighborhood give similar response# Self-Organizing Map (SOM)

• Clustering

� Often use when neighborhood of a class has significant meaning• Classification• Pattern recognition• Data mining• . . .





Training Illustration

� Neurons random initialization (cm)

� Select randomly a training sample x and find thewinning neuron cmx :

‖x− cmx‖ = minm∈{1,...,M}

‖x− cm‖

� Update the weight of the winning neuron and of itsneighborhood:

cm(t + 1) = cm(t) + hm,mx(t)[x(t)− cm(t)]

� Loop until convergence




Modification to deal with missing valueModification to deal with erroneous value

Contents








Problem: 10 dates in a MODIS time series over Brittany, France

MODIS time series (NIR band, 250m resol. 10dates). Images choosen with a cloud coverage

below 50%, zenithal angle below 20◦ overt centerof Brittany.

� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Erroneous data,clouds








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Erroneous Data,clouds








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Missing Data, sensor








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003









� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Clean Data








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Missing Data, sensor








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003









� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Clean Data








� 25-nov-2002

� 5-jan-2003

� 24-jan-2003

� 4-feb-2003

� 22-feb-2003

� 15-mar-2003

� 17-mar-2003

� 19-mar-2003

� 7-apr-2003

� 16-apr-2003

Erroneous Data,sensor





From Erroneous to Missing data

Type of errors

� Presence of clouds (± thickness)

� Presence of shadow

� Impulse noise

� outliers

Simple Cloud/Shadow Detector

Based on the Box and Whisker technique, rank statistics

let x = {x1, . . . , xk , . . .} be a time series

xk is erroneous if˛xk − α

`x3/4 − x1/4

´˛> |x1/2|, α = 1.5

Neuron definition

x = {NIR1, . . . ,NIRk , . . . ,NIR10}

where NIRi = stands for NIR band of MODIS at time i





Kohonen Map Modification

Deal with missing value

In a series x = {x1, . . . , xk , . . .}

if xk is missing ⇐⇒ k ∈Mx

Where Mx is a set that contains indices of missing components

Winning Neuron Evaluation

‖x− cm‖2 =X

j /∈Mx

“x(j)− cm(j)

”2

Winning Neuron Update cmx

cm;k(t + 1) =

(cm;k(t) + hm,mx(t)

hxk − cm;k(t)

iif k /∈Mx,

cm;k(t) if k ∈Mx.





Results

Initial NIR Band

25-nov-2002

Associated neuron value

25-nov-2002





Results

Initial NIR Band

5-jan-2003


5-jan-2003





Results

Initial NIR Band

24-jan-2003


24-jan-2003





Results

Initial NIR Band

4-feb-2003


4-feb-2003





Results

Initial NIR Band

19-mar-2003


19-mar-2003





Results

Initial NIR Band

16-apr-2003


16-apr-2003





Validation

Comparison with compositing products of MODIS/Terra

Kohonen MOD13Q1 MOD09Q1

CV-MVC through 16 days CV-MVC through 8 days

18-jan-2003 a 02-feb-2003 18-jan-2003 a 25-jan-2003





Appropriated Similarity Measure

Vanishing outiers impact

Euclidean Measure (no detection):

ED(x, y) =nX

i=1

(xi − yi )2

Euclidean Measure (with missing value):

ED(x, y) =X

i /∈Mx

(xi − yi )2

Sparse Measure:

D(x, y) =nX

i=1

|xai − y a

i |b, b > 0, a > 0





How to set parameters a and b

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5 3

Cor

rect

Mat

chin

g %

a or b

a, b = 1b, a = 1

0

20

40

60

80

100

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cor

rect

Mat

chin

g %

b

Heavy-tailed

Same distribution

0

20

40

60

80

100

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cor

rect

mat

chin

g %

b

a = 1

a =0.1

� 0 < a, b < 1.

� fit ≈ 100% when b = 0.1.

� D(x, y) =P

i |xi − yi |0.1





Comparison with other distances

a) Euclidean Distance ED(x, y) =pPn

i=1(xi − yi )2

b) Spectral Angle SA(x, y) = cos−1

„<x, y>

‖x‖ ‖y‖

«

c) Spectral Correlation SCorr(x, y) = E(xy−xyσxσy

d) Spectral Info Divergence SID(x, y) = D(x‖y) + D(y‖x)

e) Sparse Distance D(x, y) =P

i |xi − yi |0.1





Comparison with other distances

Statistiques des images de difference

a) ED b) SA c) SCorr d) SID e) Sparse D

SOM (no outlier detection at training)

µ -.03575 0.03665 0.03606 0.03878 -0.0002

σ .05594 0.13173 0.14953 0.1218 0.01607

SOM (with outlier detection at training)

µ -0.00736 -0.00233 0.00228 -0.00246 -0.00018

σ 0.03516 0.08345 0.09807 0.07718 0.01609




Contents







Generic Programming

The OTB code with Kohonen map

� Periodic SOM for training

� SOM for classification

� SOM for segmentation

typedef itk::Statistics::EuclideanDistance< VectorType >DistanceType;

typedef otb::SOMMap< VectorType, DistanceType, Dimension > MapType;typedef otb::PeriodicSOM< SampleListType, MapType,

LearningBehaviorFunctorType, NeighborhoodBehaviorFunctorType >SOMType;

SOMType::Pointer som = SOMType::New();som->SetListSample( sampleList );som->Set...som->Update();




Generic Programming






typedef otb::SOMMap< VectorType, DistanceType, Dimension > MapType;typedef otb::SOMClassifier<SampleType,SOMMapType,LabelPixelType>

ClassifierType;

ClassifierType::Pointer classifier = ClassifierType::New();classifier->SetSample(sample.GetPointer());classifier->SetMap(somreader->GetOutput());classifier->Update();




Generic Programming






typedef otb::SOMMap< VectorType, DistanceType, Dimension > MapType;typedef otb::SOMbasedImageFilter<SampleType,SOMMapType,LabelPixelType>

FilterType;

FilterType::Pointer filter = FilterType::New();filter->SetInputImage( inputImage );filter->SetMap(somReader->GetOutput());filter->Update();




Generic Programming

The OTB code with Kohonen map for missing value

� Periodic SOM for training with erroneous data

� SOM for recovering missing data

� SOM for recovering erroneous data

� SOM for what particular application?

typedef itk::Statistics::EuclideanDistance<VectorType>DistanceType;







Generic Programming






typedef otb::Statistics::EuclideanDistanceWithMissingValue<VectorType>DistanceType;







Generic Programming









typedef otb::BoxAndWhiskerImageFilter<ImageType> CloudFilterType;





Generic Programming







typedef otb::SOMMap< VectorType, DistanceType, Dimension > MapType;typedef otb::SOMbasedImageFilter<SampleType,SOMMapType,LabelPixelType>

FilterType;

FilterType::Pointer filter = FilterType::New();filter->SetInputImage( inputImage );filter->SetMap(somreader->GetOutput());filter->Update();




Generic Programming






typedef otb::Statistics::FlexibleDistanceWithMissingValue<VectorType>DistanceType;

DistanceType::SetAlphaBeta(a,b);typedef otb::SOMMap< VectorType, DistanceType, Dimension > MapType;typedef otb::SOMbasedImageFilter<SampleType,SOMMapType,LabelPixelType>

FilterType;

FilterType::Pointer filter = FilterType::New();filter->SetInputImage( inputImage );filter->SetMap(somreader->GetOutput());filter->Update();




Generic Programming






� Set your own distance

� Set the neurone type

� Set the kohonen map training procedure

� Set the Kohonen map way of using...




Implementing Kohonen’s SOM with Missing Data in OTB

Conclusion

� Generic tool for using missing and erroneous data

� Thematic part validated by the COSTEL for land use purpose

� May be adapted for many kind of supervized/unsupervised learningprocedure based on the Kohonen map.

� Just use it!


Implementing kohonen's som with missing data in OTB

Technology

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