probFDA-package: A Probabilistic Version of Fisher Linear Discriminant...

In probFDA: Probabilistic Fisher Discriminant Analysis

Description

Probabilistic Fisher discriminant analysis (pFDA) is a probabilistic version of the popular and powerful Fisher linear discriminant analysis for dimensionality reduction and classification. PFDA overcomes the known limitations of FDA in the contexts of label noise and sparse labeled data. To this end, pFDA relaxes the homoscedastic assumption on the class covariance matrices and adds a term to explicitly model the non-discriminative information. The pFDA method works at least as well as the traditional FDA method (even better in most cases) in standard situations and it clearly improves the modeling and the prediction when the dataset is subject to label noise and/or sparse labels. The practitioner may therefore replace without prejudice FDA by pFDA for its daily use.

Details

Package:	pFDA
Type:	Package
Version:	1.0
Date:	2015-01-26
License:	GPL-v2

Author(s)

Charles Bouveyron and Camille Brunet

Maintainer: Charles Bouveyron <[e-mail]>

References

C. Bouveyron and C. Brunet, Probabilistic Fisher discriminant analysis: A robust and flexible alternative to Fisher discriminant analysis, Neurocomputing, vol. 90 (1), pp. 12-22, 2012.

See Also

lda

Examples

palette(c("#E41A1C","#377EB8","#4DAF4A"))

# Simulation of data
n = 900; p = 25
n1 = 1/3*n; n2 = 1/3*n; n3 = 1/3*n; 
S1 = diag(2)
S2 = rbind(c(1,-0.95),c(-0.95,1))
S3 = rbind(c(2,0),c(0,0.05))
m1 = c(0,0); m2 = c(0,2); m3 = c(2,0)
X = rbind(mvrnorm(n1,m1,S1),mvrnorm(n2,m2,S2),mvrnorm(n3,m3,S3))
Q = qr.Q(qr(mvrnorm(p,mu=rep(0,p),Sigma=diag(25,p))))
B = mvrnorm(nrow(X),rep(0,p-2),0.1*diag(rep(p-2,p-2)))
X = crossprod(t(cbind(X,B)),Q)
cls = rep(c(1,2,3),c(n1,n2,n3))

# Cross-validation
nbrep = 10
CCR = matrix(NA,2,nbrep)
for (i in 1:nbrep){
  ind = sample(n)[1:(3/5*n)]
  lda.c = lda(X[ind,],cls[ind])
  res = predict(lda.c,X[-ind,])
  CCR[1,i] = sum(res$cl==cls[-ind])/length(cls[-ind])
  prms = pfda(X[ind,],cls[ind],model=c('DkBk','DB','AkB','AB'),crit='bic',display=TRUE)
  res = predict(prms,X[-ind,])
  CCR[2,i] = sum(res$cl==cls[-ind])/length(cls[-ind])
}

# Display results
split.screen(c(2,1))
split.screen(c(1,3), screen = 1)
screen(3)
plot(predict(princomp(X)),col=cls,pch=(17:19)[cls],main='PCA')
screen(4)
plot(crossprod(t(X),lda(X,cls)$scaling),col=cls,pch=(17:19)[cls],main='LDA')
screen(5)
plot(crossprod(t(X),pfda(X,cls,model='DkBk')$V),col=cls,pch=(17:19)[cls],main='PFDA',
  xlab='LD1',ylab='LD2')
screen(2)
boxplot(t(CCR),names=c('LDA','PFDA'),col=c(1,2),ylab="CCR",
  main='CV correct classification rate')

Example output

Loading required package: MASS
     DkBk        DB       AkB        AB 
-24998.47 -25577.96 -25224.26 -25624.22 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-24971.65 -25578.52 -25219.45 -25619.49 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25011.94 -25601.39 -25264.48 -25649.52 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25044.43 -25629.12 -25274.44 -25670.02 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-24990.91 -25593.17 -25256.43 -25639.18 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25072.25 -25639.80 -25314.97 -25683.79 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25033.56 -25628.86 -25267.72 -25677.34 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25010.45 -25585.03 -25248.35 -25631.11 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25064.93 -25651.85 -25295.11 -25684.53 
* Selected model: DkBk 
     DkBk        DB       AkB        AB 
-25048.94 -25626.77 -25288.90 -25672.22 
* Selected model: DkBk 
[1] 1 2
[1] 3 4 5

probFDA documentation built on May 1, 2019, 8:48 p.m.