Probabilistic Classifiers Using Nearest Neighbor Balls. Climate Change Workshop, Malta, March, 2009

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1 Probabilistic Classifiers Usig Nearest Neighbor Balls Climate Chage Worshop Malta March 2009 Bo Raeby & Ju Yu Cetre of Biostochastics Swedish Uiversity of Agricultural Scieces

2 Bacgroud Climate chage implies e.g. ew species compositio i the forest For assessmet of ecosystem health ad quatificatio of spatial ad temporal variatio i lad use ad ladscape patters. Remote sesig should be a useful tool BUT for the applicatios we have i mid there are problems with eistig traditioal) methods It is ecessary with a ew cocept

3 PROBLEMS AIM: Classify forest lad ad/or wetlad Overlappig feature distributios No-ormality Low accuracy Feasibility at local area Biased area estimatio

4 Data Accordig to species compositio forest lad is defied ito 32 classes I-situ measuremets Multispectral ad multitemporal satellite images give us a 12-dimesioal feature vector Spatial resolutio= piel size= 25 m

5 METHODOLOGY Defie the target fuctio i this case probabilities of correct classificatio) Deoise the images wavelet trasformatios) Remove outliers from referece data Calculate the iformatio values i the compoets i the feature vector e.g. differet bads) Determie a proper metric Determie prototypes for the classes Ru a oparametric classificatio so that the target fuctio is maimized Declare the quality of classificatio result by usig probability matrices

6 Ed-user respose The probability matrices give quality statemets o scee-level m) Not sufficiet for the ed users More local iformatio is required

7 More Quality Calculate probabilities for classes at piel level Calculate etropy for each piel

8 Noparametric Probability Estimatio Desity estimatio usig i.i.d. X X 2 1 K X Joit distributio X Y i)) X B X R i)) ) X Y ) i i i Coditioal distr. Coditioal epectatio Desity estimatio Y X = ~ ep[ g )] E[ Y i) X i = ] 1 g ) gˆ ) = 1 B R i)) d p 1 R i))

9 Noparametric Probability Estimatio cot. = = R B f where )) 1 ) ˆ Desity estimatio of class = = = j p p j j j j j j j R d R d j R B R B f f P )) 1 )) 1 ) )) )) ) ˆ ) ˆ ) class at piel π π π π π

10 The cocept of probabilistic classifiers eample - a cost-efficiet method for terrestrial moitorig Class 1 Prelimiary classificatio mied forest tree species & age 8 classes piel size m 2 3 Calculatio of pielwise probability per class Σ = 1) Calculatio of etropy red = classif. accuracy NOT OK gree yellow = OK New classificatio with improved accuracy Additioal field plots i selected areas

11 Etropy Map

12 Probability Distributio at Piel

13 Probability Map

14

15 Probabilistic Classifier Class 1) Trad. classificatio Area est.=160 Red= prob.0.8 ad gree=prob.0.4 Prob.classifier Area est.=134.4 Accuracy?????? Trad. classificatio Area est.=160 Red= prob.0.8 ad gree=prob. 0.4 Prob.classifier Area est.=134.4 Accuracy?????

16 Quality Assessmet for Cotiuous Variables Area both global ad local) amout of dead wood... Subsamplig methods to estimate the variace of sample meas sample totals ratios of meas or totals

17 Cosistet uder statioarity ad m-depedece

18 Variace Estimatio of Mea Values X A = mea of the process X } over the regio A { i j X t = mea value over the subregio t t = umber of subregios S = size of the regio A s = size of each subregio t X = 1 1 t t 1 X ) 2 X t X t s ˆ = t t γ A = Var S X A) γ ˆ γ γ 0 A

19 Errors i forest ad peatlad mass Withi the peatlad mas defied by a topographic map) about 30% is i fact forest lad Withi the forest mas defied by the same topographic map) about 6-8% is i fact peatlad As a cosequece performig the forest classificatio withi the forest mas may give misleadig results Solutio: try to mae the classificatio of forest lad ad peatlad simultaeously.

20 Forest-Peatlad mass? Iformatio from TOPO-ide ad eighborig piels Aprioriprobabilities for the classes at piel level A priori probabilites & previously calculated probabilities Aposterior probabilities for the classes at piel level New Probability Classifier The classes are aggregated up to: FOREST ad PEATLAND Calculate etropy ad determie the thresholds so that the piels belog to the followig zoes: FOREST PEATLAND or Trasitio Zoe The probability vectors are recalculated with respect to the zoes

21 Demo: mas correctio

22 Forest Peatlad & Trasitio Zoes

23 Applicatios/Modificatios Estimatio/classificatio of chages Cost-efficiet moitorig systems Idetificatio of sparse evets/ hot spot detectio Source apportiomet models itrogephosphorus leaage) Climate chage: scearios based o chages i e.g. species compositio