Kernel estimation

1. Density estimation

1.1. Histogram

1.1.1. Real world data

1.1.1.1. Galaxies

library('sm')

Package 'sm', version 2.2-6.0: type help(sm) for summary information

library(MASS)

Attachement du package : 'MASS'

L'objet suivant est masqué depuis 'package:sm':

    muscle

data(galaxies)
?galaxies
hist(galaxies)

hist(galaxies,freq=F)

hist(galaxies,freq=F,nclass=20)

hist(galaxies,breaks=quantile(galaxies,seq(0,1,len=20)))

1.1.1.2. Faithful

data(faithful)
attach(faithful)
?faithful
hist(waiting,freq=F)

hist(waiting,freq=F,nclass=20)

hist(waiting,breaks=quantile(waiting,seq(0,1,len=20)))

hist(eruptions,freq=F)

hist(eruptions,freq=F,nclass=20)

hist(eruptions,breaks=quantile(eruptions,seq(0,1,len=30)))

1.1.2. Simulation of a mixing model

rmixing=function(n,alpha,l0,l1,p0,p1)
# Generate data from a mixing model 
{
  z=rbinom(n,1,alpha)
  f1=eval(parse(text=paste('r',l1,'(',paste(c(n,p1),collapse=','),')',sep='')))
  f0=eval(parse(text=paste('r',l0,'(',paste(c(n,p0),collapse=','),')',sep='')))
  x=z*f1+(1-z)*f0
  return(x=x)
}

dmixing=function(t,alpha,l0,l1,p0,p1)
# draw the density of the mixing model
{
  res=alpha*eval(parse(text=paste('d',l1,'(t,',paste(p1,collapse=','),')',sep='')))+(1-alpha)*eval(parse(text=paste('d',l0,'(t,',paste(p0,collapse=','),')',sep='')))
}

#Example  
n=300
alpha=0.3
l0='norm'
p0=c(8,1)
l1='norm'
p1=c(0,2)
s=seq(-10,10,0.001)

x=rmixing(n,alpha,l0,l1,p0,p1)

#### histogram
par(mfrow=c(1,3))
hist(x,freq=F,ylim=c(0,0.4))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
hist(x,freq=F,ylim=c(0,0.4),nclass=20)
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
hist(x,breaks=quantile(x,seq(0,1,len=20)),ylim=c(0,0.4))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

1.2. Moving window estimator

1.2.1. On the simulated mixing model

par(mfrow=c(2,3))
plot(density(x,bw=0.001,kernel='rectangular'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=0.01,kernel='rectangular'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=0.1,kernel='rectangular'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,kernel='rectangular'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=10,kernel='rectangular'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,kernel='rectangular',bw=100),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

par(mfrow=c(1,1))
hist(x,freq=F,ylim=c(0,0.4),xlim=c(-7,12))
lines(density(x,kernel='rectangular'),col='blue')
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

1.2.2. Come back to real world data

# Galaxies 
hist(galaxies,freq=F,ylim=range(density(galaxies,kernel='rectangular')$y))
lines(density(galaxies,kernel='rectangular'),col='blue')

# Faithful 
hist(waiting,freq=F,ylim=range(density(waiting,kernel='rectangular')$y))
lines(density(waiting,kernel='rectangular'),col='blue')

hist(eruptions,freq=F,ylim=range(density(eruptions,kernel='rectangular')$y))
lines(density(eruptions,kernel='rectangular'),col='blue')

1.3. Kernel estimator

1.3.1. On the simulated mixing model

Effect of h value

par(mfrow=c(2,3))
plot(density(x,bw=0.001,kernel='g'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=0.01,kernel='g'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=0.1,kernel='g'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,kernel='g'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=10,kernel='g'),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,kernel='g',bw=100),ylim=c(0,0.4),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

par(mfrow=c(1,1))
hist(x,freq=F,ylim=c(0,0.4),xlim=c(-7,12))
lines(density(x,kernel='g'),col='blue')
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

Effect of K value

par(mfrow=c(2,3))
plot(density(x,bw=1,kernel='r'),main='Uniform',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=1,kernel='g'),main='Gaussian',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=1,kernel='e'),main='Epanechnikov',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=1,kernel='triangular'),main='Triangular',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,bw=1,kernel='b'),main='Biweight',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')
plot(density(x,kernel='cosine',bw=1),main='Cosine',ylim=c(0,0.3),xlim=c(-7,12))
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

######## Quadratic loss
# number of simulations
J=100
hs=(1:20)/20
s=seq(-10,10,0.01)

h0=5
s0=1001


QUAD_LOSS=function(s,hs,J,n,alpha,l0,l1,p0,p1,h0,s0)
{
ls= length(s)
lh=length(hs)  
EST=array(NA,c(J,ls,lh))
for (j in 1:J)
{
  x=rmixing(n,alpha,l0,l1,p0,p1)
  for (h in 1:lh) 
     {
      EST[j,,h]=sm.density(x,h=hs[h],display='none',ylim=c(0,0.4),nbins=0,eval.points=s)$estimate
     }
}
BIAS=apply(EST,c(2,3),mean)-dmixing(s,alpha,l0,l1,p0,p1)
VAR=apply(EST,c(2,3),var)
EQ=BIAS^2+VAR

nl=2
if (!is.null(s0)) nl=nl+1
  
layout(matrix(c(1:3,rep(4,3),5:(3*nl+1)),byrow=TRUE, ncol=3))
plot(hs,abs(apply(BIAS,2,mean)),type='l',ylab='|BIAS|')
plot(hs,apply(VAR,2,mean),type='l',ylab='VAR')
plot(hs,apply(EQ,2,mean),type='l',ylab='EQ')
abline(v=sm.density(x,method='normal',display="none")$h,col='blue')
abline(v=sm.density(x,method='sj',display="none")$h,col='green')
abline(v=sm.density(x,method='cv',display="none")$h,col='red')


hopt=which(apply(EQ,2,mean)==min(apply(EQ,2,mean)))
if (is.null(h0)) h0=hopt
EST2=EST[,,h0]

plot(s,EST2[1,],type='l',ylab='Estimates',main=paste('h=',hs[h0],sep=''))
for (j in 1:J) lines(s,EST2[j,])
lines(s,dmixing(s,alpha,l0,l1,p0,p1),col='red')

if (!is.null(h0)) 
  {
  plot(s,abs(BIAS[,h0]),type='l',ylab='|BIAS|',main=paste('h=',hs[h0],sep=''))
  plot(s,VAR[,h0],type='l',ylab='VAR',main=paste('h=',hs[h0],sep=''))
  plot(s,EQ[,h0],type='l',ylab='EQ',main=paste('h=',hs[h0],sep=''))
  }
if (!is.null(s0))
  {
  plot(hs,abs(BIAS[s0,]),type='l',ylab='|BIAS|',main=paste('s=',s[s0],sep=''))
  plot(hs,VAR[s0,],type='l',ylab='VAR',main=paste('s=',s[s0],sep=''))
  plot(hs,EQ[s0,],type='l',ylab='EQ',main=paste('s=',s[s0],sep=''))
  }
return(list(BIAS=BIAS,VAR=VAR,EQ=EQ,hopt=hs[hopt]))
}

RES=QUAD_LOSS(s,hs,J,n,alpha,l0,l1,p0,p1,NULL,NULL)

Automatic choice of h

plot(s,dmixing(s,alpha,l0,l1,p0,p1),col='red',type='l')
lines(density(x,kernel='e'),col='blue')
lines(density(x,bw='nrd',kernel='e'))
lines(density(x,bw='SJ',kernel='e'),col='green')
lines(density(x,bw='ucv',kernel='e'),col='orange')

Warning in bw.ucv(x): minimum occurred at one end of the range

plot(s,dmixing(s,alpha,l0,l1,p0,p1),col='red',type='l')
sm.density(x,method='normal',kernel='e',add=T)
sm.density(x,method='sj',kernel='e',col='green',add=T)
sm.density(x,method='cv',kernel='e',col='orange',add=T)

1.2.2. Come back to real world data

# Galaxies 
hist(galaxies,freq=F,ylim=range(density(galaxies,kernel='e',bw='ucv')$y))
lines(density(galaxies,kernel='rectangular',bw='ucv'),col='blue')
lines(density(galaxies,kernel='e',bw='ucv'),col='orange')

# Faithful 
hist(waiting,freq=F,ylim=range(density(waiting,kernel='e',bw='ucv')$y))
lines(density(waiting,kernel='rectangular',bw='ucv'),col='blue')
lines(density(waiting,kernel='e',bw='ucv'),col='orange')

hist(eruptions,freq=F,ylim=range(density(eruptions,kernel='e',bw='ucv')$y))
lines(density(eruptions,kernel='rectangular',bw='ucv'),col='blue')
lines(density(eruptions,kernel='e',bw='ucv'),col='orange')

## 1.4. Applications
### 1.4.1. Mode estimation

density.mode=function(x,a,b,M,bw='ucv',kernel='e',plot=T)
{
  disc=seq(a,b,length.out=M)
  dens=density(x,from=a,to=b,n=M,bw=bw,kernel=kernel)$y
  mod=disc[(order(dens))[M]]
  max=max(dens)
  if (plot) {plot(disc,dens,type='l')}
  return(list(mode=mod,max=max))
}

sm.mode=function(x,a,b,M,method='cv',plot=T)
{
  disc=seq(a,b,length.out=M)
  display="line"
  if (plot) {display="none"}
  dens=sm.density(x,eval.points=disc,method=method,nbins=0)$estimate
  mod=disc[(order(dens))[M]]
  max=max(dens)
  return(list(mode=mod,max=max))
}

plot(s,dmixing(s,alpha,l0,l1,p0,p1),col='red',type='l')
lines(density(x,bw='ucv',kernel='e'),col='orange')

Warning in bw.ucv(x): minimum occurred at one end of the range

re=density.mode(x,-10,10,1000,bw='ucv',kernel='e',F)

Warning in bw.ucv(x): minimum occurred at one end of the range

segments(re$mod,0,re$mod,re$max)
re1=density.mode(x,-10,3,1000,bw='ucv',kernel='e',F)

Warning in bw.ucv(x): minimum occurred at one end of the range

segments(re1$mod,0,re1$mod,re1$max)

1.4.1. Clustering from density level set

sm.clustering.level.sets=function(x,level=0.20,a=min(x),b=max(x),M=1000,method='sj',plot=T)
{
  disc=seq(a,b,length.out=M)
  n=length(x)
  o=order(x)
  x.and.disc=c(x,disc)
  #type=
  names(x.and.disc)=rep(c('data','disc'),c(n,M))
  x1=sort(x.and.disc)
  type1=names(x1)
  n1=length(x1)
  dens=sm.density(x,eval.points=x1,method=method,nbins=0)$estimate
  adjusted.level=quantile(dens,level)
  is.over.level=dens>adjusted.level
  cluster=rep(0,M+n)
  k=1
  for (j in 1:(M+n)) 
    {
    if (j>1) {if (is.over.level[j]==0 & is.over.level[j-1]==1 ) {k=k+1}}
    if (is.over.level[j]==1) {cluster[j]=k}
    }    
  if (plot) {plot(x1,dens,type='l')
             abline(adjusted.level,0,col='orange')}

  k=max(cluster)
  cluster.bounds=matrix(NA,2,k)
  palette=rainbow(k)
  for (j in 1:k) 
    {
      cluster.bounds[,j]=range(x1[cluster==j])
      if (plot) { segments(cluster.bounds[1,j],adjusted.level,cluster.bounds[2,j],adjusted.level,col=palette[j])}
    }
  cluster.on.data=(cluster[type1=='data'])
  #cluster.on.data[cluster.on.data==0]=NA
  return(list(cluster=cluster.on.data,cluster.bounds=cluster.bounds))
}
sm.clustering.level.sets(x,0.3)

$cluster
  [1] 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [75] 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[297] 2 0 0 0

$cluster.bounds
          [,1]      [,2]
[1,] -2.241888  5.605418
[2,]  2.595019 10.471365

1.4.2. Clustering from density extrema

sm.clustering.extrema=function(x,tau=10,a=min(x),b=max(x),M=1000,method='sj',plot=T)
{
  disc=seq(a,b,length.out=M)
  n=length(x)
  dens=sm.density(x,eval.points= disc,method=method,nbins=0)$estimate
  inc=rep(0,M)
  valleys=rep(0,M)
  k=1
  for (j in 1:M) 
    {
    i1=max(1,j-tau)
    i2=min(M,j+tau)
    ratio=(dens[i2]-dens[i1])/(disc[i2]-disc[i1])
    if (ratio>0) {inc[j]=1}
    if (j>1) {if (inc[j]==0 & inc[j-1]==1 ) {k=k+1}}
    valleys[j]=k
    }    
  if (plot) {plot(disc,dens,type='l')}

  k=max(valleys)
  thresholds=rep(NA,k)
  mins=rep(NA,k)
  for (j in 1:k) 
    {
      candidates=disc[valleys==j]
      thresholds[j]=candidates[which.min(dens[valleys==j])]
      mins[j]=min(dens[valleys==j])
      #if (plot) {segments(thresholds[j],0,thresholds[j],mins[j],col='orange')}
  }
  n=length(x)
  cluster=rep(0,n)
  for (j in 1:k) {if (j==1) {cluster[x==thresholds[j]]=j}
cluster[x>thresholds[j]]=j}
  cluster.disc=rep(0,M)
  for (j in 1:k) {if (j==1) {cluster.disc[disc==thresholds[j]]=j}
                  cluster.disc[disc>thresholds[j]]=j}
  K=max(cluster.disc)
  palette=rainbow(K+1)
  if (plot) {for (j in 0:K) {if (sum(cluster.disc==j)!=0) {
  disc.j=disc[cluster.disc==j]
                  dens.j=dens[cluster.disc==j]
                  n.j=sum(cluster.disc==j)
                  polygon(c(disc.j[1],disc.j,disc.j[n.j]),c(0,dens.j,0),
        col = palette[j+1])}  
  } }
  #cluster.on.data[cluster.on.data==0]=NA
  return(list(cluster=cluster,thresholds=thresholds))
}
sm.clustering.extrema(x,10)

$cluster
  [1] 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 1 2 2 2 1 1 2 1 2 2 2 1 2 2
 [38] 1 2 2 1 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 1 2 1 2 1 2 2 1 2 2 2 2 1 2 2 1
 [75] 2 1 1 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 2 1
[112] 2 1 2 1 2 2 1 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2 1 2 1
[149] 1 2 2 2 2 1 2 2 2 2 1 1 2 2 2 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
[186] 1 1 2 2 2 2 2 2 2 2 1 1 2 1 1 2 2 1 1 1 2 2 1 1 2 1 1 2 2 2 2 2 2 1 2 2 2
[223] 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2
[260] 2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2 1
[297] 2 2 2 2

$thresholds
[1] -3.832976  4.524096 11.599029

2. Regression estimation

2.1 Experiments

data("pressure")
t=pressure$temperature
p=pressure$pressure
plot(t,p)

res=sm.regression(t,p,method='cv')

names(res)

 [1] "eval.points" "estimate"    "model.y"     "se"          "sigma"      
 [6] "h"           "hweights"    "weights"     "data"        "call"       

res$h

[1] 7.034694

res$eval.points

 [1]   0.000000   7.346939  14.693878  22.040816  29.387755  36.734694
 [7]  44.081633  51.428571  58.775510  66.122449  73.469388  80.816327
[13]  88.163265  95.510204 102.857143 110.204082 117.551020 124.897959
[19] 132.244898 139.591837 146.938776 154.285714 161.632653 168.979592
[25] 176.326531 183.673469 191.020408 198.367347 205.714286 213.061224
[31] 220.408163 227.755102 235.102041 242.448980 249.795918 257.142857
[37] 264.489796 271.836735 279.183673 286.530612 293.877551 301.224490
[43] 308.571429 315.918367 323.265306 330.612245 337.959184 345.306122
[49] 352.653061 360.000000

res$estimate

 [1] 1.999996e-04 5.675549e-04 9.324045e-04 1.671898e-03 3.456180e-03
 [6] 5.149423e-03 1.085884e-02 1.972357e-02 2.846339e-02 4.836680e-02
[11] 7.041253e-02 9.758724e-02 1.635183e-01 2.291547e-01 3.373181e-01
[16] 5.150429e-01 6.883220e-01 1.018800e+00 1.423762e+00 1.837755e+00
[21] 2.665554e+00 3.527883e+00 4.566661e+00 6.266176e+00 7.944415e+00
[26] 1.035057e+01 1.348534e+01 1.658134e+01 2.152680e+01 2.696677e+01
[31] 3.269061e+01 4.175806e+01 5.088840e+01 6.170955e+01 7.610754e+01
[36] 9.033653e+01 1.096621e+02 1.321099e+02 1.545683e+02 1.863899e+02
[41] 2.194453e+02 2.548252e+02 3.022988e+02 3.495649e+02 4.055299e+02
[46] 4.725901e+02 5.391172e+02 6.237562e+02 7.149016e+02 8.060000e+02

n=300
x=runif(n,.1,3)
y=10*exp(-3*x)+7*cos(2*pi*x)/sqrt(x)+rnorm(n,0,2*exp(x/7))
plot(x,y)

res=sm.regression(x,y,h=.007)

res=sm.regression(x,y,h=.07)

res=sm.regression(x,y,h=.7)

res=sm.regression(x,y,method='cv')
z=seq(.1,3,len=1000)
lines(z,10*exp(-3*z)+7*cos(2*pi*z)/sqrt(z),col='red')
sm.regression(x,y,add=T,col='green')
sm.regression(x,y,add=T,col='blue',method='aicc')

names(res)

 [1] "eval.points" "estimate"    "model.y"     "se"          "sigma"      
 [6] "h"           "hweights"    "weights"     "data"        "call"       

res$h

[1] 0.05477502

res$eval.points

 [1] 0.1273684 0.1858097 0.2442510 0.3026922 0.3611335 0.4195747 0.4780160
 [8] 0.5364572 0.5948985 0.6533397 0.7117810 0.7702223 0.8286635 0.8871048
[15] 0.9455460 1.0039873 1.0624285 1.1208698 1.1793110 1.2377523 1.2961935
[22] 1.3546348 1.4130761 1.4715173 1.5299586 1.5883998 1.6468411 1.7052823
[29] 1.7637236 1.8221648 1.8806061 1.9390474 1.9974886 2.0559299 2.1143711
[36] 2.1728124 2.2312536 2.2896949 2.3481361 2.4065774 2.4650187 2.5234599
[43] 2.5819012 2.6403424 2.6987837 2.7572249 2.8156662 2.8741074 2.9325487
[50] 2.9909899

res$estimate

 [1] 20.11276678 12.45629990  5.71176184 -0.28079430 -4.42235490 -6.28804198
 [7] -6.69466615 -6.37143986 -5.26706665 -3.33710116 -1.11549263  0.91240486
[13]  3.06732639  5.34587969  7.02740926  6.76069413  5.49063965  3.73246571
[19]  1.96408487  0.04600724 -1.81258233 -3.40755684 -4.70969353 -5.71062079
[25] -6.14054995 -5.36660502 -3.66340610 -1.43509827  0.66264250  2.38432873
[31]  4.00777965  5.05853088  4.73226831  4.48533112  3.97167792  2.60929584
[37]  1.26231794 -0.34652994 -1.96030997 -3.05810007 -3.23771757 -3.11169427
[43] -2.91278296 -2.36164057 -1.36826755 -0.02259091  1.74685948  3.12868144
[49]  3.93435717  5.22962117

res=sm.regression(x,y,method='cv',eval.points=sort(x))

plot(res$estimate,y[order(x)])
abline(0,1)

2.2 Compute CV

Compute_CV=function(x,y,method,weights=NA)
{
  hopt=sm.regression(x,y,method=method,display='none')$h
  n=length(x)
  if (is.na(weights)) weights=rep(1,n)
  CV=0
  for (i in 1:n)
  {
    CV=CV+(y[i]-sm.regression(x[-i],y[-i],h=hopt,eval.points=x[i],display='none')$estimate)^2*weights[i] 
  }
  return(CV)
}
Compute_CV(x,y,'cv')

[1] 1828.23

2.3 Discrimination

load('Dopage.RData')
hema

 [1] 35.81801 57.69442 54.68696 45.73142 57.02237 57.03312 46.94246 51.21867
 [9] 37.23734 44.22872 43.19019 55.46140 48.31791 43.52074 44.31600 46.83335
[17] 43.98864 45.58534 40.67590 41.64725 46.58286 45.40957 46.14132 41.32432
[25] 51.92825 57.57791 45.10522 49.81766 54.59558 59.94339 46.68741 45.03787
[33] 43.78030 44.32881 47.85452 55.01740 49.64086 44.75317 53.80269 41.54966
[41] 52.33685 43.40389 57.02227 45.73978 56.13190 56.19256 45.33341 56.38840
[49] 45.36690 55.29222 42.93230 44.22211 48.11121 44.84885 46.35119 49.09645
[57] 46.76331 50.31146 44.09170 59.08955 42.67297 47.43126 54.06605 56.46029
[65] 39.68902 52.62125 45.54387 45.69921 53.13572 43.71261 34.72460 48.33640
[73] 51.22310 39.82190 45.93546

test

 [1] "negatif" "positif" "positif" "negatif" "positif" "positif" "negatif"
 [8] "negatif" "negatif" "negatif" "negatif" "positif" "positif" "negatif"
[15] "negatif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
[22] "negatif" "negatif" "negatif" "negatif" "positif" "negatif" "positif"
[29] "positif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
[36] "positif" "negatif" "negatif" "positif" "negatif" "negatif" "negatif"
[43] "positif" "negatif" "positif" "positif" "negatif" "positif" "negatif"
[50] "positif" "negatif" "negatif" "positif" "negatif" "negatif" "negatif"
[57] "negatif" "negatif" "negatif" "positif" "negatif" "negatif" "positif"
[64] "positif" "negatif" "positif" "negatif" "negatif" "positif" "negatif"
[71] "negatif" "negatif" "positif" "negatif" "negatif"

ROC Curve

####### ROC 
ROC=function(z,p1,plot=FALSE)
{
  p=c(-0.0001,sort(unique(p1)),1.0001)#seq(-0.01,1.01,0.01)c(-0.0001,sort(unique(p1))-0.00000000001,1.0001)
  lp=length(p)
  ROC=matrix(NA,lp,2)
  for (s in 1:lp)
  {
    ROC[s,1]=mean(p1[z==0]>=p[s])
    ROC[s,2]=mean(p1[z==1]>=p[s])  
  }
  #AUC=sum((ROC[-(lp),2])*(ROC[-(lp),1]-ROC[-(1),1]))
  AUC=sum((ROC[-(lp),2]+ROC[-1,2])*(ROC[-(lp),1]-ROC[-(1),1])/2)
  
  colnames(ROC)=c("FPR","TPR")
  if (plot)  
  {
    plot(ROC,type='l',main=paste('AUC =', AUC))
    abline(0,1,col='orange')
  }
  
  return(list(ROC=ROC,AUC=AUC))
}

Estimated Bayes estimator

#######
Classif_NP=function(X,Y,X0=NA,plot=FALSE)
{
  X=as.matrix(X)
  n=length(Y)
  V=sort(unique(Y))
  n_V=length(V)
  Prob=matrix(NA,n,n_V)
  colnames(Prob)=V
  Class=rep(NA,n)
  if (!is.na(max(X0)))
  {
    X0=as.matrix(X0)
    P0=matrix(NA,nrow(X0),n_V)
    Class0=rep(NA,n)
  }
  for (v in 1:n_V)
  {
    z=as.numeric(Y==V[v])
    for (i in 1:n )
    {
      value=sm.regression(X[-i,],z[-i], eval.points=X,eval.grid=FALSE,display='none',method='cv')$estimate[i]
      if (!is.na(value)) {Prob[i,v]=value}
      if (is.na(value)) {Prob[i,v]=mean(z[-i])}
      }
    if (!is.na(max(X0))) {P0[,v]=sm.regression(X,z,eval.points=X0,eval.grid=FALSE,display='none',method='cv')$estimate
                          P0[is.na(P0[,v]),v]=mean(z)}
  }
  if (n_V==2) {Roc=ROC(Y==V[2],Prob[,2],plot)}
  Class=V[apply(Prob,1,which.max)]
  V_est=sort(unique(Class))
  if (length(V_est)==n_V){M_table=table(Y,Class)}
  else {
    M_table=matrix(0,n_V,n_V)
    M_table0=table(Y,Class)
    for (j in 1:length(V_est)) {M_table[,which(V==V_est[j])]=M_table0[,j]}
  }
  Err=1-(sum(diag(M_table))/sum(M_table))
  if (!is.na(max(X0))) {Class0=V[apply(P0,1,which.max)]}
  if (!is.na(max(X0))) {return(list(Class=Class, Prob=Prob, M_table=M_table, Err=Err, Class0=Class0,Prob0=P0,Auc=ifelse(n_V==2,Roc$AUC,NA)))}
  else {return(list(Class=Class, Prob=Prob, M_table=M_table, Err=Err,Auc=ifelse(n_V==2,Roc$AUC,NA)))}
}


(R=Classif_NP(hema,test))

$Class
 [1] "negatif" "positif" "positif" "negatif" "positif" "positif" "negatif"
 [8] "positif" "negatif" "negatif" "negatif" "positif" "negatif" "negatif"
[15] "negatif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
[22] "negatif" "negatif" "negatif" "positif" "positif" "negatif" "negatif"
[29] "positif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
[36] "positif" "negatif" "negatif" "positif" "negatif" "positif" "negatif"
[43] "positif" "negatif" "positif" "positif" "negatif" "positif" "negatif"
[50] "positif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
[57] "negatif" "negatif" "negatif" "positif" "negatif" "negatif" "positif"
[64] "positif" "negatif" "positif" "negatif" "negatif" "positif" "negatif"
[71] "negatif" "negatif" "negatif" "negatif" "negatif"

$Prob
          negatif       positif
 [1,]  1.00154507 -0.0015450745
 [2,] -0.04382121  1.0438212062
 [3,]  0.15434486  0.8456551429
 [4,]  0.90091255  0.0990874512
 [5,] -0.01638242  1.0163824152
 [6,] -0.01690106  1.0169010600
 [7,]  0.81826853  0.1817314683
 [8,]  0.44026871  0.5597312871
 [9,]  1.00271923 -0.0027192346
[10,]  0.97256267  0.0274373255
[11,]  0.99912319  0.0008768104
[12,]  0.08722628  0.9127737158
[13,]  0.74966874  0.2503312641
[14,]  0.99257122  0.0074287785
[15,]  0.96949129  0.0305087136
[16,]  0.85954431  0.1404556941
[17,]  0.98031247  0.0196875314
[18,]  0.90954426  0.0904557440
[19,]  1.01159987 -0.0115998736
[20,]  1.01219351 -0.0121935133
[21,]  0.84465421  0.1553457920
[22,]  0.91948677  0.0805132308
[23,]  0.87502350  0.1249764977
[24,]  1.01244526 -0.0124452622
[25,]  0.37195543  0.6280445651
[26,] -0.03976347  1.0397634697
[27,]  0.93550456  0.0644954388
[28,]  0.70593566  0.2940643421
[29,]  0.16263064  0.8373693607
[30,] -0.10987017  1.1098701736
[31,]  0.83712560  0.1628744014
[32,]  0.93883629  0.0611637069
[33,]  0.98622358  0.0137764204
[34,]  0.96902890  0.0309710958
[35,]  0.74592644  0.2540735614
[36,]  0.12494026  0.8750597443
[37,]  0.58845052  0.4115494755
[38,]  0.95204114  0.0479588551
[39,]  0.23653296  0.7634670375
[40,]  1.01233017 -0.0123301720
[41,]  0.33199241  0.6680075853
[42,]  0.99507654  0.0049234647
[43,] -0.01637771  1.0163777104
[44,]  0.90040899  0.0995910059
[45,]  0.03615177  0.9638482341
[46,]  0.03197847  0.9680215341
[47,]  0.92364019  0.0763598122
[48,]  0.01908133  0.9809186730
[49,]  0.92182592  0.0781740837
[50,]  0.10130621  0.8986937855
[51,]  1.00314294 -0.0031429360
[52,]  0.97278976  0.0272102447
[53,]  0.76563576  0.2343642391
[54,]  0.94776350  0.0522365039
[55,]  0.86088772  0.1391122774
[56,]  0.63806219  0.3619378147
[57,]  0.83158518  0.1684148177
[58,]  0.52611805  0.4738819468
[59,]  0.97711055  0.0228894489
[60,] -0.07255244  1.0725524359
[61,]  1.00631785 -0.0063178519
[62,]  0.78037033  0.2196296735
[63,]  0.21164314  0.7883568648
[64,]  0.01457321  0.9854267891
[65,]  1.00865833 -0.0086583277
[66,]  0.35111770  0.6488822958
[67,]  0.91193400  0.0880660046
[68,]  0.90284398  0.0971560181
[69,]  0.30071516  0.6992848429
[70,]  0.98798550  0.0120145043
[71,]  1.00131155 -0.0013115545
[72,]  0.70514409  0.2948559066
[73,]  0.69715038  0.3028496153
[74,]  1.00909475 -0.0090947457
[75,]  0.88832274  0.1116772601

$M_table
         Class
Y         negatif positif
  negatif      47       3
  positif       5      20

$Err
[1] 0.1066667

$Auc
[1] 0.7456

plot(hema,R$Prob[,2])

Classif_NP(hema,test,c(37,42,58,57))

$Class
 [1] "negatif" "positif" "positif" "negatif" "positif" "positif" "negatif"
 [8] "positif" "negatif" "negatif" "negatif" "positif" "negatif" "negatif"
[15] "negatif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
[22] "negatif" "negatif" "negatif" "positif" "positif" "negatif" "negatif"
[29] "positif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
[36] "positif" "negatif" "negatif" "positif" "negatif" "positif" "negatif"
[43] "positif" "negatif" "positif" "positif" "negatif" "positif" "negatif"
[50] "positif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
[57] "negatif" "negatif" "negatif" "positif" "negatif" "negatif" "positif"
[64] "positif" "negatif" "positif" "negatif" "negatif" "positif" "negatif"
[71] "negatif" "negatif" "negatif" "negatif" "negatif"

$Prob
          negatif       positif
 [1,]  1.00154507 -0.0015450745
 [2,] -0.04382121  1.0438212062
 [3,]  0.15434486  0.8456551429
 [4,]  0.90091255  0.0990874512
 [5,] -0.01638242  1.0163824152
 [6,] -0.01690106  1.0169010600
 [7,]  0.81826853  0.1817314683
 [8,]  0.44026871  0.5597312871
 [9,]  1.00271923 -0.0027192346
[10,]  0.97256267  0.0274373255
[11,]  0.99912319  0.0008768104
[12,]  0.08722628  0.9127737158
[13,]  0.74966874  0.2503312641
[14,]  0.99257122  0.0074287785
[15,]  0.96949129  0.0305087136
[16,]  0.85954431  0.1404556941
[17,]  0.98031247  0.0196875314
[18,]  0.90954426  0.0904557440
[19,]  1.01159987 -0.0115998736
[20,]  1.01219351 -0.0121935133
[21,]  0.84465421  0.1553457920
[22,]  0.91948677  0.0805132308
[23,]  0.87502350  0.1249764977
[24,]  1.01244526 -0.0124452622
[25,]  0.37195543  0.6280445651
[26,] -0.03976347  1.0397634697
[27,]  0.93550456  0.0644954388
[28,]  0.70593566  0.2940643421
[29,]  0.16263064  0.8373693607
[30,] -0.10987017  1.1098701736
[31,]  0.83712560  0.1628744014
[32,]  0.93883629  0.0611637069
[33,]  0.98622358  0.0137764204
[34,]  0.96902890  0.0309710958
[35,]  0.74592644  0.2540735614
[36,]  0.12494026  0.8750597443
[37,]  0.58845052  0.4115494755
[38,]  0.95204114  0.0479588551
[39,]  0.23653296  0.7634670375
[40,]  1.01233017 -0.0123301720
[41,]  0.33199241  0.6680075853
[42,]  0.99507654  0.0049234647
[43,] -0.01637771  1.0163777104
[44,]  0.90040899  0.0995910059
[45,]  0.03615177  0.9638482341
[46,]  0.03197847  0.9680215341
[47,]  0.92364019  0.0763598122
[48,]  0.01908133  0.9809186730
[49,]  0.92182592  0.0781740837
[50,]  0.10130621  0.8986937855
[51,]  1.00314294 -0.0031429360
[52,]  0.97278976  0.0272102447
[53,]  0.76563576  0.2343642391
[54,]  0.94776350  0.0522365039
[55,]  0.86088772  0.1391122774
[56,]  0.63806219  0.3619378147
[57,]  0.83158518  0.1684148177
[58,]  0.52611805  0.4738819468
[59,]  0.97711055  0.0228894489
[60,] -0.07255244  1.0725524359
[61,]  1.00631785 -0.0063178519
[62,]  0.78037033  0.2196296735
[63,]  0.21164314  0.7883568648
[64,]  0.01457321  0.9854267891
[65,]  1.00865833 -0.0086583277
[66,]  0.35111770  0.6488822958
[67,]  0.91193400  0.0880660046
[68,]  0.90284398  0.0971560181
[69,]  0.30071516  0.6992848429
[70,]  0.98798550  0.0120145043
[71,]  1.00131155 -0.0013115545
[72,]  0.70514409  0.2948559066
[73,]  0.69715038  0.3028496153
[74,]  1.00909475 -0.0090947457
[75,]  0.88832274  0.1116772601

$M_table
         Class
Y         negatif positif
  negatif      47       3
  positif       5      20

$Err
[1] 0.1066667

$Class0
[1] "negatif" "negatif" "positif" "positif"

$Prob0
            [,1]         [,2]
[1,]  1.00181472 -0.001814722
[2,]  1.01045534 -0.010455342
[3,] -0.04880557  1.048805567
[4,] -0.01445100  1.014450998

$Auc
[1] 0.7456

3. Multivariate and Functional case

3.1 Multivariate case

3.1.1 Regression

load('Randonnee.RData')
library(knitr)
library(kableExtra)

kable(cbind(long,lat,alti),'html',caption="Data given in Randonnee.RData") %>%
  kable_styling() %>%
  scroll_box(width = "100%", height='7cm')

Data given in Randonnee.RData

long	lat	alti
99.0624679	53.3076627	1503.552
-6.8700422	28.2190488	1565.064
-3.9917884	92.2394410	1523.288
31.8887100	-9.1710346	1495.187
20.8955966	25.1860652	1612.269
15.3682732	80.5044866	1511.161
11.4690357	88.5174201	1503.051
79.8319344	102.4300348	1535.229
56.0075673	107.6692620	1503.432
29.4260498	16.7352382	1573.805
-4.3391908	102.0056042	1478.104
72.7352515	32.1038612	1557.071
80.2107291	0.1943822	1509.054
13.0087572	93.5295195	1519.488
17.4792537	-7.7909738	1517.155
35.5514487	5.6133995	1532.295
13.5712102	25.8517935	1614.147
2.0481796	-7.4330306	1508.660
22.9454398	27.9979667	1606.543
36.9931913	31.7602686	1551.006
17.0726327	80.8224924	1498.533
97.9897970	77.7829623	1547.869
100.2870167	61.8244704	1510.328
105.5622748	106.6027542	1507.775
21.9907795	12.9867447	1559.080
46.8235776	29.8245296	1565.675
45.4129347	61.9143907	1490.260
34.3569008	93.7161598	1505.586
35.6348959	-3.0641687	1517.431
42.1465047	90.6220438	1496.808
54.9246438	71.5075653	1522.724
-0.6032085	107.4425999	1503.936
38.9608041	79.0489369	1504.162
107.5811816	23.9735269	1519.739
52.8454450	100.7978796	1512.662
50.1340882	-0.9997788	1531.310
7.7555722	32.0321676	1648.128
-5.8852304	3.6869886	1522.290
105.2549906	78.7011588	1518.597
47.1467618	66.8373312	1522.303
-4.6626037	92.5977188	1479.269
8.7576174	34.3697844	1641.704
52.2500823	13.6763844	1536.718
-7.6250490	-0.9289558	1501.063
36.5993508	54.0141936	1499.579
92.0424269	84.5729018	1555.299
103.4379530	33.0318845	1510.353
50.7240071	2.2425787	1509.026
97.4716941	77.9736253	1515.126
73.7016949	99.7308117	1536.054
93.0219061	67.1765613	1547.277
65.6176874	98.6371979	1526.580
-1.3699311	73.6878124	1495.551
52.3760663	78.5963519	1530.826
84.7114132	42.2642248	1495.388
107.5771911	48.0871036	1506.657
64.4604991	27.6326412	1591.445
59.9686836	51.0937702	1505.332
8.4859424	75.3498196	1493.466
60.8453952	81.6616607	1542.620
32.6244900	26.3138900	1555.251
109.0847392	29.1766504	1516.603
72.0450547	19.7782183	1586.880
62.9426072	27.6257777	1591.079
49.7946765	51.4461836	1512.832
-3.7844638	108.6813870	1496.539
14.6025297	102.8902643	1511.974
68.9487006	98.7188453	1524.002
19.4557040	103.9766379	1498.990
23.4424702	91.6052843	1507.005
96.9559850	17.2084007	1540.036
17.4085176	16.5421165	1569.178
7.6359436	93.0814601	1499.439
105.9557061	88.8294518	1510.976
-0.6395778	27.0807526	1583.589
40.0386443	95.0945388	1494.300
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89.4257922	46.7036010	1519.883
61.1501857	38.6312221	1523.934
3.1689991	21.9017038	1571.345
54.2624584	75.0700301	1520.234
-2.1329539	0.6990997	1517.794
14.5326373	14.6623044	1569.137
92.0923677	14.5583923	1540.265
50.9768518	11.4237147	1523.812
25.7224895	62.8373531	1499.869
9.0913331	91.3946745	1497.405
56.7395689	65.3898101	1526.841
-6.9715546	108.3857356	1505.603
86.1255730	37.8573761	1513.962
7.6243359	-5.6062683	1508.418
14.3570259	78.8911665	1492.319
78.8684186	86.3794514	1701.078
50.1203243	6.5330506	1525.042
78.2810920	101.1884724	1548.463
91.9315635	32.0111449	1514.694
-1.8781652	45.9827446	1553.455
19.2320025	48.2957502	1577.783
52.5425185	5.6003292	1518.864
5.5162289	101.0176554	1511.460
68.3529132	96.7494079	1542.238
29.1369224	15.5334408	1544.346
-3.6228530	94.7946062	1485.693
80.2698530	-8.4745485	1514.719
63.7084272	92.6554637	1534.721
5.0221692	5.5771130	1521.852
23.1965916	22.3894481	1595.744
107.4721211	61.1590065	1511.029
91.2873364	85.5051300	1557.369
35.2431964	29.0336821	1547.582
67.6516760	10.0403570	1512.336
88.2066043	14.8927116	1537.623
69.6267306	84.3787444	1594.476

library(plotly)

Le chargement a nécessité le package : ggplot2

Attachement du package : 'ggplot2'

L'objet suivant est masqué _par_ '.GlobalEnv':

    Position

Attachement du package : 'plotly'

L'objet suivant est masqué depuis 'package:ggplot2':

    last_plot

L'objet suivant est masqué depuis 'package:MASS':

    select

L'objet suivant est masqué depuis 'package:stats':

    filter

L'objet suivant est masqué depuis 'package:graphics':

    layout

library(sm)
longitude=seq(min(long),max(long),length=100)
latitude=seq(min(lat),max(lat),length=100)
RES=sm.regression(cbind(long,lat),alti,eval.points=cbind(longitude,latitude), eval.grid=TRUE,method='cv',display='none')$estimate
Est_altitude=matrix(RES,100,100)
DT=data.frame(longitude,latitude,Est_altitude)
plot_ly(DT,x=~latitude,y=~longitude,z = ~Est_altitude, type = "surface")

#%>%   layout(xaxis = list(autorange = "reversed"))

Estimated.Altitude=sm.regression(cbind(long,lat),alti,eval.points=Position, eval.grid=FALSE,method='cv',display='none')$estimate
lo=Position[,1]
la=Position[,2]
DT2=data.frame(Time,lo,la,Estimated.Altitude)
plot_ly(DT,x=~latitude,y=~longitude,z = ~Est_altitude, type = "surface")%>%
add_trace(x=~la,y=~lo,z = ~Estimated.Altitude, type = "scatter3d",mode='markers')

plot_ly(DT2,x=~Time,y=~Estimated.Altitude, type = 'scatter', mode = 'lines')

#plot_ly(DT2,x=~la,y=~lo,z = ~RES, type = "scatter3d",trace='add')
#%>%   layout(xaxis = list(autorange = "reversed"))

3.2.2 Discrimination

load('Jussac.RData')
library(knitr)
library(kableExtra)

kable(cbind(Type,LCB,LMS,LBM,LP,LM,LAM),'html',caption="Data given in Jussac.RData") %>%
  kable_styling() %>%
  scroll_box(width = "100%", height='7cm')

Data given in Jussac.RData

Type	LCB	LMS	LBM	LP	LM	LAM
1	129	64	95	17.5	11.2	13.8
1	154	74	76	20.0	14.2	16.5
1	170	87	71	17.9	12.3	15.9
1	188	94	73	19.5	13.3	14.8
1	161	81	55	17.1	12.1	13.0
1	164	90	58	17.5	12.7	14.7
1	203	109	65	20.7	14.0	16.8
1	178	97	57	17.3	12.8	14.3
1	212	114	65	20.5	14.3	15.5
1	221	123	62	21.2	15.2	17.0
1	183	97	52	19.3	12.9	13.5
1	212	112	65	19.7	14.2	16.0
1	220	117	70	19.8	14.3	15.6
1	216	113	72	20.5	14.4	17.7
1	216	112	75	19.6	14.0	16.4
1	205	110	68	20.8	14.1	16.4
1	228	122	78	22.5	14.2	17.8
1	218	112	65	20.3	13.9	17.0
1	190	93	78	19.7	13.2	14.0
1	212	111	73	20.5	13.7	16.6
1	201	105	70	19.8	14.3	15.9
1	196	106	67	18.5	12.6	14.2
1	158	71	71	16.7	12.5	13.3
1	255	126	86	21.4	15.0	18.0
1	234	113	83	21.3	14.8	17.0
1	205	105	70	19.0	12.4	14.9
1	186	97	62	19.0	13.2	14.2
1	241	119	87	21.0	14.7	18.3
1	220	111	88	22.5	15.4	18.0
1	242	120	85	19.9	15.3	17.6
3	199	105	73	23.4	15.0	19.1
3	227	117	77	25.0	15.3	18.6
3	228	122	82	24.7	15.0	18.5
3	232	123	83	25.3	16.8	15.5
3	231	121	78	23.5	16.5	19.6
3	215	118	74	25.7	15.7	19.0
3	184	100	69	23.3	15.8	19.7
3	175	94	73	22.2	14.8	17.0
3	239	124	77	25.0	16.8	27.0
3	203	109	70	23.3	15.0	18.7
3	226	118	72	26.0	16.0	19.4
3	226	119	77	26.5	16.8	19.3

Quant=cbind(LCB,LMS,LBM,LP,LM,LAM)

choice=combn(1:6,2)
NC=ncol(choice)
for (j in 1:NC)
{
  x=Quant[,choice[,j]]
  ju=Jussac[choice[,j]]
  print(colnames(x))
  print(Classif_NP(x,Type,ju))
}

[1] "LCB" "LMS"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Loup  Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Chien Chien Loup  Chien Chien Chien
[37] Chien Chien Chien Chien Chien Chien
Levels: Chien Jussac Loup

$Prob
          Chien         Loup
 [1,] 0.9968071  0.003192929
 [2,] 1.0396700 -0.039670038
 [3,] 0.8711861  0.128813903
 [4,] 0.9114322  0.088567841
 [5,] 0.9256400  0.074360023
 [6,] 0.6479006  0.352099411
 [7,] 0.5958009  0.404199089
 [8,] 0.6427308  0.357269248
 [9,] 0.5284826  0.471517429
[10,] 0.1008899  0.899110081
[11,] 0.7340450  0.265955012
[12,] 0.6196508  0.380349220
[13,] 0.5273338  0.472666184
[14,] 0.6415822  0.358417824
[15,] 0.6826343  0.317365693
[16,] 0.5871850  0.412814999
[17,] 0.4072262  0.592773809
[18,] 0.7127609  0.287239090
[19,] 0.9767716  0.023228367
[20,] 0.6613262  0.338673787
[21,] 0.7241818  0.275818245
[22,] 0.6002263  0.399773727
[23,] 1.2721424 -0.272142439
[24,] 0.6115807  0.388419343
[25,] 0.9283272  0.071672824
[26,] 0.7841586  0.215841352
[27,] 0.7815437  0.218456342
[28,] 0.7142495  0.285750511
[29,] 0.7817515  0.218248484
[30,] 0.7313537  0.268646280
[31,] 0.7280969  0.271903065
[32,] 0.6883376  0.311662387
[33,] 0.4915187  0.508481306
[34,] 0.5081294  0.491870592
[35,] 0.5773703  0.422629739
[36,] 0.6483357  0.351664251
[37,] 0.7237995  0.276200468
[38,] 0.8072750  0.192724995
[39,] 0.5818795  0.418120549
[40,] 0.7581497  0.241850325
[41,] 0.6250374  0.374962581
[42,] 0.5827946  0.417205426

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup      11      0    1

$Err
[1] 0.3095238

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]       [,2]
[1,] 0.9431089 0.05689111

$Auc
[1] 0.5861111

[1] "LCB" "LBM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Loup  Chien Loup  Chien Loup  Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Chien Loup  Chien Chien Loup  Chien
[37] Chien Chien Loup  Chien Chien Loup 
Levels: Chien Jussac Loup

$Prob
          Chien         Loup
 [1,] 1.7941288 -0.794128819
 [2,] 0.7788844  0.221115627
 [3,] 0.6426749  0.357325061
 [4,] 0.5500336  0.449966389
 [5,] 1.0404019 -0.040401922
 [6,] 0.9633000  0.036699981
 [7,] 0.9217973  0.078202680
 [8,] 0.9908199  0.009180114
 [9,] 0.9671192  0.032880827
[10,] 1.1715196 -0.171519632
[11,] 1.1499001 -0.149900088
[12,] 0.9671192  0.032880827
[13,] 0.6564391  0.343560892
[14,] 0.5907119  0.409288116
[15,] 0.4829629  0.517037142
[16,] 0.7948145  0.205185547
[17,] 0.3265101  0.673489942
[18,] 0.9592956  0.040704405
[19,] 0.4434532  0.556546752
[20,] 0.5615024  0.438497562
[21,] 0.6804689  0.319531134
[22,] 0.7788681  0.221131923
[23,] 0.8067945  0.193205498
[24,] 1.1761676 -0.176167625
[25,] 0.5417162  0.458283805
[26,] 0.6968803  0.303119737
[27,] 0.8959084  0.104091638
[28,] 0.9177806  0.082219445
[29,] 0.7820513  0.217948687
[30,] 0.7579148  0.242085246
[31,] 0.6762616  0.323738441
[32,] 0.4509495  0.549050524
[33,] 0.6399355  0.360064477
[34,] 0.6827756  0.317224357
[35,] 0.4315022  0.568497838
[36,] 0.5926531  0.407346880
[37,] 0.8065273  0.193472736
[38,] 0.8378498  0.162150157
[39,] 0.4297505  0.570249523
[40,] 0.7669815  0.233018465
[41,] 0.6363004  0.363699568
[42,] 0.4614977  0.538502267

$M_table
        Class
Y        Chien Jussac Loup
  Chien     27      0    3
  Jussac     0      0    0
  Loup       8      0    4

$Err
[1] 0.2619048

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.6338983 0.3661017

$Auc
[1] 0.5805556

[1] "LCB" "LP" 
$Class
 [1] Chien Loup  Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Loup  Loup  Loup  Loup  Chien Loup 
[37] Loup  Loup  Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,]  1.000000000 -3.402009e-26
 [2,]  0.134541725  8.654583e-01
 [3,]  0.998576475  1.423525e-03
 [4,]  0.958623019  4.137698e-02
 [5,]  1.000104133 -1.041328e-04
 [6,]  0.999686013  3.139871e-04
 [7,]  0.848168511  1.518315e-01
 [8,]  1.003595517 -3.595517e-03
 [9,]  0.971498030  2.850197e-02
[10,]  0.913305985  8.669402e-02
[11,]  0.988090217  1.190978e-02
[12,]  1.011132675 -1.113268e-02
[13,]  1.015954426 -1.595443e-02
[14,]  0.985735396  1.426460e-02
[15,]  1.014525335 -1.452533e-02
[16,]  0.848469751  1.515302e-01
[17,]  0.595281242  4.047188e-01
[18,]  1.000917407 -9.174067e-04
[19,]  0.939660213  6.033979e-02
[20,]  0.971498030  2.850197e-02
[21,]  0.988473935  1.152607e-02
[22,]  1.010433450 -1.043345e-02
[23,]  1.000263286 -2.632863e-04
[24,]  0.810934779  1.890652e-01
[25,]  0.921095265  7.890473e-02
[26,]  1.012330725 -1.233072e-02
[27,]  0.992210077  7.789923e-03
[28,]  0.968746819  3.125318e-02
[29,]  0.544725908  4.552741e-01
[30,]  1.073350138 -7.335014e-02
[31,]  0.092848287  9.071517e-01
[32,]  0.063628544  9.363715e-01
[33,]  0.122885364  8.771146e-01
[34,] -0.002361877  1.002362e+00
[35,]  0.545244135  4.548052e-01
[36,] -0.045940159  1.045940e+00
[37,] -0.212893305  1.212893e+00
[38,]  0.292479009  7.075210e-01
[39,] -0.058326860  1.058327e+00
[40,]  0.197557601  8.024424e-01
[41,] -0.019099470  1.019099e+00
[42,] -0.036862879  1.036863e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     29      0    1
  Jussac     0      0    0
  Loup       1      0   11

$Err
[1] 0.04761905

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.9630371 0.0369629

$Auc
[1] 0.6555556

[1] "LCB" "LM" 
$Class
 [1] Chien Loup  Chien Chien Chien Chien Chien Chien Chien Loup  Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Loup  Chien Loup  Chien Chien Loup  Loup  Chien
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
              Chien          Loup
 [1,]  1.0000000000 -3.590287e-21
 [2,]  0.0957844879  9.042155e-01
 [3,]  1.0000000002 -2.100731e-10
 [4,]  0.9998079685  1.920315e-04
 [5,]  1.0000000000 -4.829945e-12
 [6,]  0.9999999031  9.694703e-08
 [7,]  1.0071266387 -7.126639e-03
 [8,]  0.9999999452  5.481227e-08
 [9,]  0.9319331918  6.806681e-02
[10,]  0.4877520748  5.122479e-01
[11,]  1.0000005158 -5.158245e-07
[12,]  0.9775954241  2.240458e-02
[13,]  0.9395988870  6.040111e-02
[14,]  0.8977249684  1.022750e-01
[15,]  1.0026028477 -2.602848e-03
[16,]  0.9847949805  1.520502e-02
[17,]  1.0507846013 -5.078460e-02
[18,]  1.0040736371 -4.073637e-03
[19,]  0.9999946113  5.388734e-06
[20,]  1.0047089428 -4.708943e-03
[21,]  0.7036228145  2.963772e-01
[22,]  1.0000000021 -2.121634e-09
[23,]  0.9999999999  8.075307e-11
[24,]  1.0472226527 -4.722265e-02
[25,]  0.8365726205  1.634274e-01
[26,]  0.9999999996  4.329199e-10
[27,]  0.9999448330  5.516703e-05
[28,]  0.9778640777  2.213592e-02
[29,]  0.3437279543  6.562720e-01
[30,]  0.6803879730  3.196120e-01
[31,]  0.4163297477  5.836703e-01
[32,]  0.5796864845  4.203135e-01
[33,]  0.7574011078  2.425989e-01
[34,] -0.0003649075  1.000365e+00
[35,]  0.0083537536  9.916462e-01
[36,]  0.9394903785  6.050963e-02
[37,] -0.1559031242  1.155903e+00
[38,]  0.5086558818  4.913441e-01
[39,]  0.0014215707  9.985784e-01
[40,]  0.4490770128  5.509230e-01
[41,]  0.2380195946  7.619804e-01
[42,] -0.0009418316  1.000942e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     27      0    3
  Jussac     0      0    0
  Loup       4      0    8

$Err
[1] 0.1666667

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
         [,1]         [,2]
[1,] 1.002257 -0.002257412

$Auc
[1] 0.7333333

[1] "LCB" "LAM"
$Class
 [1] Chien Loup  Loup  Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Loup  Loup  Loup  Chien Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
              Chien          Loup
 [1,]   1.000107378 -1.073780e-04
 [2,] -35.064982969  3.606498e+01
 [3,]   0.485695218  5.143048e-01
 [4,]   0.977496896  2.250310e-02
 [5,]   1.000069523 -6.952280e-05
 [6,]   0.987691434  1.230857e-02
 [7,]   0.813406745  1.865933e-01
 [8,]   0.993403714  6.596286e-03
 [9,]   0.938884536  6.111546e-02
[10,]   0.896018217  1.039818e-01
[11,]   1.001407574 -1.407574e-03
[12,]   0.975308174  2.469183e-02
[13,]   0.634098528  3.659015e-01
[14,]   0.657943120  3.420569e-01
[15,]   0.950372911  4.962709e-02
[16,]   0.972855994  2.714401e-02
[17,]   0.685738029  3.142620e-01
[18,]   0.914538832  8.546117e-02
[19,]   1.000988869 -9.888690e-04
[20,]   0.973178194  2.682180e-02
[21,]   0.983060307  1.693969e-02
[22,]   1.000750338 -7.503382e-04
[23,]   0.999997845  2.155482e-06
[24,]   1.458273181 -4.582732e-01
[25,]   0.813096944  1.869031e-01
[26,]   0.982951464  1.704854e-02
[27,]   0.999256095  7.439048e-04
[28,]   0.614743986  3.852560e-01
[29,]   0.541680862  4.583191e-01
[30,]   0.999177628  8.223715e-04
[31,]  -0.012323031  1.012323e+00
[32,]   0.385451937  6.145481e-01
[33,]   0.460535104  5.394649e-01
[34,]   1.019302353 -1.930235e-02
[35,]  -0.095647511  1.095648e+00
[36,]   0.067755790  9.322442e-01
[37,]  -0.157020719  1.157021e+00
[38,]   0.999275365  1.198849e-03
[39,]  -0.003647941  1.003648e+00
[40,]   0.222875772  7.771242e-01
[41,]  -0.079138579  1.079139e+00
[42,]  -0.023749794  1.023750e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       2      0   10

$Err
[1] 0.0952381

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]       [,2]
[1,] 0.9635584 0.03644162

$Auc
[1] 0.6736111

[1] "LMS" "LBM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Loup 
[25] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Loup  Chien
[37] Chien Chien Loup  Chien Chien Loup 
Levels: Chien Jussac Loup

$Prob
          Chien        Loup
 [1,] 1.4394796 -0.43947957
 [2,] 0.9412932  0.05870681
 [3,] 0.7681495  0.23185050
 [4,] 0.6305956  0.36940441
 [5,] 1.0984759 -0.09847590
 [6,] 0.9652619  0.03473807
 [7,] 0.9126600  0.08734002
 [8,] 1.0103298 -0.01032976
 [9,] 0.9351001  0.06489987
[10,] 1.1592268 -0.15922680
[11,] 1.1505786 -0.15057861
[12,] 0.9323131  0.06768694
[13,] 0.6128769  0.38712307
[14,] 0.5801157  0.41988428
[15,] 0.5226151  0.47738492
[16,] 0.7723066  0.22769338
[17,] 0.1353025  0.86469749
[18,] 0.9323131  0.06768694
[19,] 0.6789587  0.32104128
[20,] 0.5629352  0.43706480
[21,] 0.6653289  0.33467105
[22,] 0.7972834  0.20271660
[23,] 1.1124567 -0.11245670
[24,] 0.3078150  0.69218497
[25,] 0.7703063  0.22969370
[26,] 0.6653289  0.33467105
[27,] 0.8853278  0.11467215
[28,] 0.8371818  0.16281818
[29,] 1.3792849 -0.37928491
[30,] 0.6559248  0.34407519
[31,] 0.6730716  0.32692842
[32,] 0.5068424  0.49315757
[33,] 0.5144496  0.48555044
[34,] 0.5664894  0.43351060
[35,] 0.3889101  0.61108988
[36,] 0.5094019  0.49059809
[37,] 0.8043109  0.19568910
[38,] 0.8338612  0.16613882
[39,] 0.2902466  0.70975344
[40,] 0.7421588  0.25784122
[41,] 0.6004308  0.39956921
[42,] 0.4459567  0.55404327

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       9      0    3

$Err
[1] 0.2619048

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.6363852 0.3636148

$Auc
[1] 0.5694444

[1] "LMS" "LP" 
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Loup  Chien Loup  Loup  Loup  Loup  Chien Loup 
[37] Loup  Loup  Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
              Chien          Loup
 [1,]  7.073171e-01  0.000000e+00
 [2,]  8.213317e-01  1.786683e-01
 [3,]  9.997883e-01  2.116830e-04
 [4,]  9.534227e-01  4.657729e-02
 [5,]  1.000008e+00 -7.720626e-06
 [6,]  1.000076e+00 -7.645688e-05
 [7,]  9.303569e-01  6.964305e-02
 [8,]  1.000220e+00 -2.199508e-04
 [9,]  9.938211e-01  6.178891e-03
[10,]  9.789227e-01  2.107728e-02
[11,]  9.891281e-01  1.087194e-02
[12,]  1.003492e+00 -3.491864e-03
[13,]  1.005449e+00 -5.448592e-03
[14,]  9.910253e-01  8.974663e-03
[15,]  1.003504e+00 -3.503567e-03
[16,]  9.318504e-01  6.814963e-02
[17,]  4.384134e-01  5.615085e-01
[18,]  9.960116e-01  3.988394e-03
[19,]  8.916444e-01  1.083556e-01
[20,]  9.812575e-01  1.874246e-02
[21,]  9.879072e-01  1.209282e-02
[22,]  1.001629e+00 -1.628801e-03
[23,]  1.000000e+00 -2.196221e-07
[24,]  9.886692e-01  1.133081e-02
[25,]  8.768034e-01  1.231966e-01
[26,]  1.001951e+00 -1.950877e-03
[27,]  9.983103e-01  1.689712e-03
[28,]  9.754970e-01  2.450298e-02
[29,]  4.012648e-01  5.987352e-01
[30,]  1.009789e+00 -9.789196e-03
[31,]  7.264794e-02  9.273521e-01
[32,]  1.302973e-12  1.000000e+00
[33,]  7.922616e-02  9.207738e-01
[34,] -8.258978e-03  1.008259e+00
[35,]  5.348084e-01  4.651249e-01
[36,]  1.650124e-03  9.983499e-01
[37,] -1.899749e-01  1.189975e+00
[38,]  2.093153e-01  7.906847e-01
[39,]  1.195267e-02  9.880473e-01
[40,]  2.817952e-01  7.182048e-01
[41,] -2.661182e-03  1.002661e+00
[42,] -7.817637e-03  1.007818e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       1      0   11

$Err
[1] 0.07142857

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.8624162 0.1375838

$Auc
[1] 0.7611111

[1] "LMS" "LM" 
$Class
 [1] Chien Loup  Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Loup  Chien Loup  Chien Chien Loup  Loup  Loup 
[37] Loup  Loup  Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
            Chien          Loup
 [1,]  1.01069929 -0.0106992918
 [2,]  0.20243149  0.7975685129
 [3,]  1.03903304 -0.0390330372
 [4,]  0.88527350  0.1147264983
 [5,]  1.02504741 -0.0250474141
 [6,]  0.99924296  0.0007570422
 [7,]  0.88909139  0.1109086065
 [8,]  1.02490376 -0.0249037615
 [9,]  0.88382512  0.1161748792
[10,]  0.62430414  0.3756958554
[11,]  1.00802892 -0.0080289183
[12,]  0.87914247  0.1208575348
[13,]  0.95234038  0.0476596154
[14,]  0.81700784  0.1829921648
[15,]  0.95849324  0.0415067641
[16,]  0.87294003  0.1270599691
[17,]  1.12950539 -0.1295053881
[18,]  0.99524501  0.0047549934
[19,]  0.90767345  0.0923265534
[20,]  1.03841469 -0.0384146895
[21,]  0.66283640  0.3371636016
[22,]  1.11796989 -0.1179698916
[23,]  0.94184526  0.0581547444
[24,]  0.77059645  0.2294035459
[25,]  0.62919578  0.3708042178
[26,]  1.24724022 -0.2472402166
[27,]  0.94168638  0.0583136194
[28,]  0.80929593  0.1907040664
[29,]  0.24280533  0.7571946659
[30,]  0.52344695  0.4765530515
[31,]  0.43399122  0.5660087778
[32,]  0.53197113  0.4680288681
[33,]  0.84729678  0.1527032214
[34,] -0.05142195  1.0514219525
[35,]  0.05283981  0.9471601899
[36,]  0.36298431  0.6370156877
[37,] -0.24535586  1.2453558641
[38,]  0.39492693  0.6050730672
[39,] -0.02294511  1.0229451116
[40,]  0.49977694  0.5002230628
[41,]  0.22050620  0.7794938022
[42,] -0.16475575  1.1647557466

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       2      0   10

$Err
[1] 0.0952381

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.7724708 0.2275292

$Auc
[1] 0.6416667

[1] "LMS" "LAM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Loup 
[25] Chien Chien Chien Loup  Loup  Chien Loup  Loup  Chien Chien Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
              Chien          Loup
 [1,]  1.000000e+00 -2.109889e-08
 [2,]  9.531285e-01  4.687147e-02
 [3,]  6.717125e-01  3.282875e-01
 [4,]  9.598445e-01  4.015551e-02
 [5,]  1.000071e+00 -7.064228e-05
 [6,]  1.001949e+00 -1.949123e-03
 [7,]  9.339045e-01  6.609551e-02
 [8,]  9.985148e-01  1.485209e-03
 [9,]  8.548089e-01  1.451911e-01
[10,]  7.678428e-01  2.321572e-01
[11,]  1.001966e+00 -1.965804e-03
[12,]  9.749288e-01  2.507116e-02
[13,]  6.305578e-01  3.694422e-01
[14,]  7.021250e-01  2.978750e-01
[15,]  9.828330e-01  1.716703e-02
[16,]  9.934115e-01  6.588502e-03
[17,]  7.567813e-01  2.432187e-01
[18,]  9.347093e-01  6.529070e-02
[19,]  1.002546e+00 -2.546269e-03
[20,]  9.842375e-01  1.576249e-02
[21,]  9.258548e-01  7.414517e-02
[22,]  9.939020e-01  6.098045e-03
[23,]  1.000000e+00 -4.012877e-07
[24,]  4.076343e-01  5.923657e-01
[25,]  9.319928e-01  6.800715e-02
[26,]  9.987467e-01  1.253331e-03
[27,]  9.999496e-01  5.036889e-05
[28,]  3.295119e-01  6.590382e-01
[29,]  4.972126e-01  5.027874e-01
[30,]  8.256132e-01  1.743868e-01
[31,]  1.035903e-01  8.964097e-01
[32,]  3.922032e-01  6.077968e-01
[33,]  5.883643e-01  4.116357e-01
[34,]  1.023880e+00 -2.388002e-02
[35,] -2.143617e-01  1.214362e+00
[36,]  1.511650e-01  8.488350e-01
[37,] -3.599950e-01  1.359995e+00
[38,]  8.232866e-01  1.767134e-01
[39,] -8.677953e-05  1.000087e+00
[40,]  3.213723e-01  6.786277e-01
[41,] -1.039122e-01  1.103912e+00
[42,] -1.564087e-02  1.015641e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     27      0    3
  Jussac     0      0    0
  Loup       3      0    9

$Err
[1] 0.1428571

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.6542453 0.3457547

$Auc
[1] 0.7875

[1] "LBM" "LP" 
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Loup  Loup  Loup  Loup  Chien Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,]  1.000019753 -1.975302e-05
 [2,]  0.980853685  1.914632e-02
 [3,]  1.000447584 -4.475844e-04
 [4,]  1.002423405 -2.423405e-03
 [5,]  1.000000089 -8.922781e-08
 [6,]  0.999999942  5.771260e-08
 [7,]  0.945526700  5.447330e-02
 [8,]  1.000000085 -8.491915e-08
 [9,]  0.975391525  2.460848e-02
[10,]  0.859826131  1.401739e-01
[11,]  0.999976613  2.338708e-05
[12,]  1.003043320 -3.043320e-03
[13,]  0.989718663  1.028134e-02
[14,]  0.858619108  1.413809e-01
[15,]  1.008214265 -8.214265e-03
[16,]  0.834794690  1.652053e-01
[17,]  0.029962841  9.931038e-01
[18,]  0.990913428  9.086572e-03
[19,]  1.028070078 -2.807008e-02
[20,]  0.855753065  1.442469e-01
[21,]  0.989718663  1.028134e-02
[22,]  1.001245139 -1.245139e-03
[23,]  1.000148314 -1.483141e-04
[24,]  0.987108335  1.289166e-02
[25,]  0.922798455  7.720155e-02
[26,]  1.002633329 -2.633329e-03
[27,]  1.000175568 -1.755679e-04
[28,]  1.018471071 -1.847107e-02
[29,]  0.685209489  3.147905e-01
[30,]  1.030694845 -3.069484e-02
[31,]  0.128269574  8.717304e-01
[32,]  0.022513394  9.774866e-01
[33,]  0.144506967  8.554930e-01
[34,] -0.012779433  1.012779e+00
[35,]  0.575555485  4.244445e-01
[36,] -0.003354162  1.003354e+00
[37,]  0.080760580  9.192394e-01
[38,]  0.548653198  4.513468e-01
[39,]  0.022513394  9.774866e-01
[40,]  0.058112137  9.418879e-01
[41,] -0.012248954  1.012249e+00
[42,] -0.020606376  1.020606e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     29      0    1
  Jussac     0      0    0
  Loup       2      0   10

$Err
[1] 0.07142857

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]      [,2]
[1,] 0.8792215 0.1207785

$Auc
[1] 0.6111111

[1] "LBM" "LM" 
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Loup  Loup  Chien Chien Loup  Loup 
[37] Loup  Loup  Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,]  1.006267278 -6.267278e-03
 [2,]  0.837977693  1.620223e-01
 [3,]  1.000017102 -1.710184e-05
 [4,]  0.997925637  2.074363e-03
 [5,]  1.000000003 -3.104118e-09
 [6,]  0.999999970  3.018117e-08
 [7,]  1.006374765 -6.374765e-03
 [8,]  0.999999883  1.169261e-07
 [9,]  0.941696974  5.830303e-02
[10,]  0.514238557  4.857614e-01
[11,]  1.000000012 -1.152800e-08
[12,]  0.975014745  2.498525e-02
[13,]  0.810642337  1.893577e-01
[14,]  0.676109358  3.238906e-01
[15,]  0.944273438  5.572656e-02
[16,]  0.976878679  2.312132e-02
[17,]  0.883728678  1.162713e-01
[18,]  1.009338134 -9.338134e-03
[19,]  1.035786657 -3.578666e-02
[20,]  0.996829363  3.170637e-03
[21,]  0.810642337  1.893577e-01
[22,]  1.000027833 -2.783275e-05
[23,]  0.999999293  7.065808e-07
[24,]  0.933654853  6.634515e-02
[25,]  0.761215898  2.387841e-01
[26,]  1.000010233 -1.023271e-05
[27,]  0.999925709  7.429136e-05
[28,]  1.440744196 -4.407442e-01
[29,]  1.351458374 -3.514584e-01
[30,]  0.708027304  2.919727e-01
[31,]  0.269828188  7.301718e-01
[32,]  0.309883664  6.901163e-01
[33,]  0.771335724  2.286643e-01
[34,]  0.816009272  1.839907e-01
[35,]  0.002536301  9.974637e-01
[36,]  0.029838852  9.701611e-01
[37,]  0.235212890  7.647871e-01
[38,]  0.426114402  5.738856e-01
[39,] -0.002457640  1.002458e+00
[40,]  0.427975936  5.720241e-01
[41,]  0.001168787  9.988312e-01
[42,] -0.002457640  1.002458e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     30      0    0
  Jussac     0      0    0
  Loup       2      0   10

$Err
[1] 0.04761905

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]       [,2]
[1,] 0.9682595 0.03174052

$Auc
[1] 0.7722222

[1] "LBM" "LAM"
$Class
 [1] Loup  Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Loup  Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Chien Chien Loup  Loup  Chien Chien Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,] -3.579416170  4.579416e+00
 [2,]  0.765246547  2.347535e-01
 [3,]  0.884158467  1.158415e-01
 [4,]  0.954840827  4.515917e-02
 [5,]  1.008238835 -8.238835e-03
 [6,]  0.995831740  4.168260e-03
 [7,]  0.787938023  2.120620e-01
 [8,]  1.001041265 -1.041265e-03
 [9,]  0.971226766  2.877323e-02
[10,]  0.749698151  2.503018e-01
[11,]  1.000000000 -1.142315e-45
[12,]  0.922289623  7.771038e-02
[13,]  0.930774329  6.922567e-02
[14,]  0.487317728  5.126823e-01
[15,]  0.781505021  2.184950e-01
[16,]  0.836444002  1.635560e-01
[17,]  0.522478742  4.775213e-01
[18,]  0.740526358  2.594736e-01
[19,]  0.796968174  2.030318e-01
[20,]  0.754847777  2.451522e-01
[21,]  0.894496897  1.055031e-01
[22,]  1.030437062 -3.043706e-02
[23,]  1.049693908 -4.969391e-02
[24,]  0.768927177  2.310728e-01
[25,]  0.773897253  2.261027e-01
[26,]  0.988721815  1.127819e-02
[27,]  1.015506234 -1.550623e-02
[28,]  0.765370904  2.346291e-01
[29,]  0.883021908  1.169781e-01
[30,]  0.781165533  2.188345e-01
[31,]  0.101888153  8.981118e-01
[32,]  0.334254184  6.657458e-01
[33,]  0.576304456  4.236955e-01
[34,]  1.077379764 -7.737976e-02
[35,] -0.002347413  1.002347e+00
[36,]  0.144088231  8.559118e-01
[37,] -0.140710392  1.140710e+00
[38,]  0.732115031  2.678850e-01
[39,] -2.348756299  3.348756e+00
[40,]  0.267267277  7.327327e-01
[41,] -0.014428943  1.014429e+00
[42,]  0.094590505  9.054095e-01

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       3      0    9

$Err
[1] 0.1190476

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
         [,1]     [,2]
[1,] 0.755392 0.244608

$Auc
[1] 0.7152778

[1] "LP" "LM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Loup  Chien Loup  Loup  Loup  Loup  Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,]  1.000022595 -2.259530e-05
 [2,]  1.005035517 -5.035517e-03
 [3,]  1.000076728 -7.672811e-05
 [4,]  0.993512566  6.487434e-03
 [5,]  1.000050860 -5.085980e-05
 [6,]  1.000121969 -1.219693e-04
 [7,]  0.885991413  1.140086e-01
 [8,]  1.000142292 -1.422916e-04
 [9,]  0.944521550  5.547845e-02
[10,]  0.807924675  1.920753e-01
[11,]  0.996321263  3.678737e-03
[12,]  1.033042623 -3.304262e-02
[13,]  1.034794443 -3.479444e-02
[14,]  0.949579590  5.042041e-02
[15,]  1.020030080 -2.003008e-02
[16,]  0.870812350  1.291876e-01
[17,] -0.213390647  1.213391e+00
[18,]  0.954680594  4.531941e-02
[19,]  0.987922901  1.207710e-02
[20,]  0.909319997  9.068000e-02
[21,]  1.034794443 -3.479444e-02
[22,]  0.999862706  1.372936e-04
[23,]  1.000097186 -9.718628e-05
[24,]  0.761915520  2.380845e-01
[25,]  0.787581288  2.124187e-01
[26,]  0.999371075  6.289251e-04
[27,]  0.999394667  6.053326e-04
[28,]  0.860148610  1.398514e-01
[29,]  0.374506283  6.254937e-01
[30,]  1.285507830 -2.855078e-01
[31,]  0.331165858  6.688341e-01
[32,]  0.005905740  9.940943e-01
[33,]  0.062633030  9.373670e-01
[34,] -0.005396005  1.005396e+00
[35,]  0.360209395  6.397906e-01
[36,] -0.041047550  1.041048e+00
[37,]  0.359614887  6.403851e-01
[38,]  0.711055638  2.889444e-01
[39,]  0.003254312  9.967457e-01
[40,]  0.352040844  6.479592e-01
[41,] -0.041956042  1.041956e+00
[42,] -0.048680399  1.048680e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       1      0   11

$Err
[1] 0.07142857

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]       [,2]
[1,] 0.9381193 0.06188067

$Auc
[1] 0.6972222

[1] "LP"  "LAM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Loup  Chien Chien Chien Chien Chien Chien Chien
[25] Chien Chien Chien Chien Loup  Chien Loup  Loup  Loup  Loup  Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
              Chien          Loup
 [1,]  1.000255e+00 -2.546781e-04
 [2,]  9.951940e-01  4.806018e-03
 [3,]  1.007967e+00 -7.966628e-03
 [4,]  9.901074e-01  9.892572e-03
 [5,]  1.000183e+00 -1.825095e-04
 [6,]  1.000664e+00 -6.638512e-04
 [7,]  9.202638e-01  7.973624e-02
 [8,]  1.000364e+00 -3.638306e-04
 [9,]  8.987586e-01  1.012414e-01
[10,]  8.221209e-01  1.778791e-01
[11,]  9.978787e-01  2.121330e-03
[12,]  9.953817e-01  4.618319e-03
[13,]  9.821855e-01  1.781447e-02
[14,]  1.000442e+00 -4.418637e-04
[15,]  1.013108e+00 -1.310780e-02
[16,]  8.768309e-01  1.231691e-01
[17,]  4.819352e-01  5.180648e-01
[18,]  9.914723e-01  8.527663e-03
[19,]  9.869788e-01  1.302125e-02
[20,]  9.430705e-01  5.692945e-02
[21,]  9.878487e-01  1.215130e-02
[22,]  9.999518e-01  4.818591e-05
[23,]  1.000129e+00 -1.289290e-04
[24,]  7.882186e-01  2.117814e-01
[25,]  7.955892e-01  2.044108e-01
[26,]  9.983084e-01  1.691617e-03
[27,]  9.982625e-01  1.737471e-03
[28,]  8.686287e-01  1.313713e-01
[29,]  4.802339e-01  5.197661e-01
[30,]  1.086552e+00 -8.655181e-02
[31,]  2.067179e-01  7.932821e-01
[32,]  8.261469e-02  9.173853e-01
[33,]  1.328166e-01  8.671834e-01
[34,] -3.359782e-05  1.001543e+00
[35,]  2.860779e-02  9.713922e-01
[36,] -1.051961e-02  1.010520e+00
[37,]  3.371560e-02  9.662844e-01
[38,]  9.912356e-01  8.764378e-03
[39,] -6.391207e-01  1.639121e+00
[40,]  3.150334e-01  6.849666e-01
[41,] -5.278270e-02  1.052783e+00
[42,] -5.132187e-02  1.051322e+00

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       1      0   11

$Err
[1] 0.07142857

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]       [,2]
[1,] 0.9514529 0.04854711

$Auc
[1] 0.6611111

[1] "LM"  "LAM"
$Class
 [1] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[13] Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien Chien
[25] Loup  Chien Chien Loup  Chien Chien Loup  Loup  Loup  Loup  Loup  Loup 
[37] Loup  Chien Loup  Loup  Loup  Loup 
Levels: Chien Jussac Loup

$Prob
             Chien          Loup
 [1,]  1.000000000 -8.444785e-21
 [2,]  0.946957631  5.304237e-02
 [3,]  0.999999984  1.584453e-08
 [4,]  0.999991162  8.838320e-06
 [5,]  1.000000000 -1.652703e-17
 [6,]  0.999999999  1.364058e-09
 [7,]  0.997233368  2.766632e-03
 [8,]  1.000000000  1.116284e-10
 [9,]  1.013049223 -1.304922e-02
[10,]  0.834250689  1.657493e-01
[11,]  1.000000000 -5.188620e-12
[12,]  0.994780937  5.219063e-03
[13,]  1.001479611 -1.479611e-03
[14,]  0.871425895  1.285741e-01
[15,]  1.011524881 -1.152488e-02
[16,]  0.989412666  1.058733e-02
[17,]  1.015272729 -1.527273e-02
[18,]  1.018226781 -1.822678e-02
[19,]  0.999999992  7.655264e-09
[20,]  1.035495613 -3.549561e-02
[21,]  0.965453913  3.454609e-02
[22,]  1.000000000 -1.570561e-11
[23,]  1.000000000 -7.055253e-15
[24,]  0.563149934  4.368501e-01
[25,]  0.047757173  9.522453e-01
[26,]  1.000000000 -1.376477e-10
[27,]  0.999999959  4.091530e-08
[28,]  0.447797917  5.522021e-01
[29,]  0.589745874  4.102541e-01
[30,]  0.846136437  1.538636e-01
[31,] -0.295358448  1.295358e+00
[32,]  0.334758812  6.652412e-01
[33,]  0.410713121  5.892869e-01
[34,]  0.055612685  9.443873e-01
[35,] -0.015501642  1.015502e+00
[36,]  0.200930943  7.990691e-01
[37,] -0.219924842  1.219925e+00
[38,]  1.000049336 -4.930692e-05
[39,] -2.310839328  3.310839e+00
[40,]  0.240858384  7.591416e-01
[41,]  0.014449831  9.855502e-01
[42,]  0.006676652  9.933233e-01

$M_table
        Class
Y        Chien Jussac Loup
  Chien     28      0    2
  Jussac     0      0    0
  Loup       1      0   11

$Err
[1] 0.07142857

$Class0
[1] Chien
Levels: Chien Jussac Loup

$Prob0
          [,1]        [,2]
[1,] 0.9988722 0.001127843

$Auc
[1] 0.7194444

3.2 Functional case

3.2.1 Regression

fdaplot=function(X,ylim=NULL)
{
  matplot(t(X),type='l',ylim=ylim)
}

library("fda")

Le chargement a nécessité le package : splines

Le chargement a nécessité le package : fds

Le chargement a nécessité le package : rainbow

Le chargement a nécessité le package : pcaPP

Le chargement a nécessité le package : RCurl

Le chargement a nécessité le package : deSolve

Attachement du package : 'fda'

L'objet suivant est masqué depuis 'package:graphics':

    matplot

TECATOR=read.table('npfda-spectrometric.dat')
CURVES=as.matrix(TECATOR[,-101])
Y=TECATOR[,101]
fdaplot(CURVES)

source('npfda.R')
R0=funopare.kernel.cv(Y,CURVES, CURVES,0,10,c(0,1))
R0$Mse

[1] 117.2638

plot(R0$Estimated.values,Y)
abline(0,1)

R1=funopare.kernel.cv(Y,CURVES, CURVES,1,10,c(0,1))
R1$Mse

[1] 44.27052

plot(R1$Estimated.values,Y)
abline(0,1)

R2=funopare.kernel.cv(Y,CURVES, CURVES,2,10,c(0,1))
R2$Mse

[1] 5.784178

plot(R2$Estimated.values,Y)
abline(0,1)

R3=funopare.kernel.cv(Y,CURVES, CURVES,3,10,c(0,1))
R3$Mse

[1] 9.118275

plot(R3$Estimated.values,Y)
abline(0,1)

Rpca=funopare.kernel.cv(Y,CURVES, CURVES,semimetric='pca',10)
Rpca$Mse

[1] 122.7028

plot(Rpca$Estimated.values,Y)
abline(0,1)

3.2.2 Discrimination

load("PHONEMES.RData")
par(mfrow=c(2,3))
Phon=sort(unique(PHONEME))
for (j in Phon)
{
fdaplot(CURVES[PHONEME==j,],ylim=range(CURVES))
title(j)
}

#######
Classif_NP_fun=function(X,Y,X0=NA,plot=FALSE,semimetric,...)
{
  X=as.matrix(X)
  X0=as.matrix(X0)
  n=length(Y)
  V=sort(unique(Y))
  n_V=length(V)
  Prob=matrix(NA,n,n_V)
  colnames(Prob)=V
  Class=rep(NA,n)
  test_sample=FALSE
  if (!is.na(max(X0)) & (any(dim(X)!=dim(X0)))) 
  {
    test_sample=TRUE
  }
  if (!is.na(max(X0)) & (all(dim(X)==dim(X0)))) 
  {
    if (any(X!=X0)){test_sample=TRUE}
  }
  if (test_sample)
  {
    P0=matrix(NA,nrow(X0),n_V)
    Class0=rep(NA,n)
  }
  for (v in 1:n_V)
  {
    z=as.numeric(Y==V[v])
    Prob[,v]=funopare.kernel.cv(z,X,X,semimetric=semimetric,...)$Estimated.values
    if (test_sample) {P0[,v]=funopare.kernel.cv(z,X,X0,semimetric=semimetric,...)$Predicted.values}
  }
  if (n_V==2) {Roc=ROC(Y==V[2],Prob[,2],plot)}
  Class=V[apply(Prob,1,which.max)]
  V_est=sort(unique(Class))
  if (length(V_est)==n_V){M_table=table(Y,Class)}
  else {
    M_table=matrix(0,n_V,n_V)
    M_table0=table(Y,Class)
    for (j in 1:length(V_est)) {M_table[,which(V==V_est[j])]=M_table0[,j]}
  }
  Err=1-(sum(diag(M_table))/sum(M_table))
  if (test_sample) {Class0=V[apply(P0,1,which.max)]}
  if (test_sample) {return(list(Class=Class, Prob=Prob, M_table=M_table, Err=Err, Class0=Class0,Prob0=P0,Auc=ifelse(n_V==2,Roc$AUC,NA)))}
  else {return(list(Class=Class, Prob=Prob, M_table=M_table, Err=Err,Auc=ifelse(n_V==2,Roc$AUC,NA)))}
}

learn=1:1000
RE=Classif_NP_fun(CURVES[learn,],PHONEME[learn],CURVES[-learn,],semimetric = 'mplsr',q=4)
RE$M_table

     Class
Y      AA  AO DCL  IY  SH
  AA  153  47   0   0   0
  AO   26 173   1   0   0
  DCL   0   0 199   1   0
  IY    0   0   1 199   0
  SH    0   0   0   0 200

table(PHONEME[-learn],RE$Class0)

     
       AA  AO DCL  IY  SH
  AA  152  48   0   0   0
  AO   29 171   0   0   0
  DCL   1   0 199   0   0
  IY    0   0   0 200   0
  SH    0   0   0   0 200