模式識(shí)別計(jì)算題

一、

Giventheinformationasbelow:

SampleNo.

123

123

Feature1

112

-1-1-2

Feature2

10-1

10-1

Class

1

2

Thendecidingthesamplex=(00)’belongingtowhichclassusingthetheoryofminimumerrorprobability

First:(1)computingthemeanofthefirstclassbasedonthegiveninformation

Second:(1)computingthecovarianceofthefirstclassbasedonthegiveninformation

Third：decidingthesamplexbelongingtowhichclassusingthetheoryofminimumerrorprobability

二、

Iftheobserveddatafollowstheuniformdistributionwithunknownθ1andθ2:

Determinationofparametersθ1andθ2usingmaximumlikelihoodestimates.

First:extractingNsamplesindependentlyandachievingthecorrespondinglikelihoodfunction

Second:theformofthelog-likelihoodfunctionis

Third:theformofthepartialderivativeforthelog-likelihoodfunctionis

Fourth:themaximumlikelihoodestimationofθ1andθ2are:

Whereisthexmaximumandxminimumwithinallsamples.

三、PrincipalComponentAnalysis

Theinformationofthetrainingsetisdescribedasfollows:

UsingPCAapproachtocompletethedimensionalityreduction.

Firststep:Computingthemeanoftheithclassmiandthemeanofallclassm.

Secondstep:ComputingtheoveralldivergencematrixSt.

Thirdstep:CompletingtheSingularvaluedecompositionofoveralldivergencematrixSt.

Fourthstep:

Fifthstep:SincethetransformationmatrixWonlycontainonecolumnvector,itisnoneedtoobtainingtheStandardizedorthogonaltransformationmatrix.

Sixthstep:Obtainingtheprincipalcomponent:

四、LinearDiscriminantAnalysis

ComputetheLinearDiscriminantprojectionforthefollowingtwo-dimensionaldataset.

SampleNo.

123

123

Feature1

112

-1-1-2

Feature2

10-1

10-1

Class

1

2

Firststep:Computingthemeanofeachclass

Fourthstep:ObtainingtheLADprojection

五、NearestNeighborClassification

IftheinformationofthetrainingsamplesTandthetestingsamplex(0.20.2)aredescribedasfollowsrespectively:

SampleNo.

123

123

123

Feature1

0.20.40.2

0.20.20.2

000.5

Feature2

0.10.20.5

0.40.40.4

0.20.20.2

Class

1

2

3

Trytodeterminatethetypeofxusingthek-nearestneighbormethod.

Thefirststep:Eachtrainingsampleisfirstconsideredasatemplate.

Thesecondstep:Computingthedistancebetweenthetestingsampleandeachtemplate

x(0.2,0.2)

Herewecountthenumberofminimum=0.2foreachclassKi,i=1,2,3

Thefourthstep:AssigningthetypeofthemaximumKitothetestingsample.

x=2

六、

Iftheinformationofseveralunknowntypesamplesis:

Trytousek-Ltransformationtoreducethedimensionalityofsamplex=(x1,x2)’.

Thefirststep:Computingthecovariancematrix

Thesecondstep:Computingthecovariancematrix’seigenvaluesandcorrespondingeigenvectors;

Thethirdstep:GeneratingthetransformationmatrixTbasedontheeigenvectorsforthetopNorthogonaleigenvalues

CompletingK-Ltransformation

七、AnexampleofK-meansalgorithm

Iftheinformationofonedatasetisdescribedasbelow:

SampleNo.

123456

Feature1

010121

Feature2

001112

UsingtheK-meansalgorithmtoclusterthisdatasetintotwoclasses

1.Dividingsamplesintopreset2classesandchoosingx1andx2asthecenterofclass1and2respectively:

2.ComputingtheEuclideandistanceofallsamplestoeachclass’scenter;

3.AssigningeachsampletotheappreciateclassbasedontheruleofminimumEuclideandistance

5.Ifthecurrentcenterofeachclassisthesameasthepriorsameclass,thentheK-meansalgorithmisfinished;otherwise,returntothestep2、3、4,andmakeadecisionwhethertheconditionoffinishissatisfied.

5.Ifthecurrentcenterofeachclassisthesameasthepriorsameclass,thentheK-meansalgorithmisfinished.

Iftheinformationofdatasetisdescribedasfollows:

UsingthePartitionalclusteringalgorithmtoclusterthisdatasetintooneclass.

1.Considering6sampleas6classes

ComputingthesquaredEuclideandistancebetweenallclasses

Searchingtheminimum

clusteringcorrespondingc