VHDClassification-package: Discrimination-Classification in very high dimension with...
In VHDClassification: Discrimination/Classification in very high dimension with linear and quadratic rules.
Description
Details
Author(s)
References
Examples
Description
This package provides an implementation of Linear disciminant analysis
and quadratic discriminant analysis that works fine in very high dimension
(when there are many more variables than observations).
Details
Package: VHDClassification
Type: Package
Version: 0.1
Date: 2010-04-15
License: GPL-2
LazyLoad: yes
Depends: methods, e1071, lattice, stats
This package provides learning procedure for classification in very high dimension.
Binary learning is done with learnBinaryRule while K-class (K>=2) learning is done
with function learnPartitionWithLLR.
learnBinaryRule can return an object LinearRule-class or an object QuadraticRule-class depending
whether type='linear' or 'quadratic'.
learnPartitionWithLLR basically returns a set of binary rules which is represented by the class PartitionWithLLR-class.
The used procedure for the learning are described in the papers cited below. The
The method predict (predict-methods) is implemented for class LinearRule-class QuadraticRule-class learnPartitionWithLLR.
It predicts the class of a new observation.
Author(s)
Maintainer-author: Robin Girard <robin.girard@mines-paristech.fr>
References
Fast rate of convergence in high dimensional linear discriminant analysis. R. Girard To appear in Journal of Nonparametric Statistics.\
Very high dimensional discriminant analysis with thresholding estimation. R. Girard. Submitted.
Examples
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############ Tests 2 classes when the true rule should be quadratic
#library(VHDClassification)
p=500; n=50 ; mu=array(0,c(p,2)) ; C=array(c(1,20),c(p,2)); C[c(1,3,5),1]=40
x=NULL; y=NULL;
for (k in 1:2)
{
M=matrix(rnorm(p*n),nrow=p,ncol=n)
tmp=array(C[,k]^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))
x=rbind(x,t(tmp));
y=c(y,array(k,n))
}
#Learning
LearnedQuadBinaryRule=learnBinaryRule(x,y,type='quadratic')
LearnedLinBinaryRule=learnBinaryRule(x,y) # default is linear type
# for comparison with SVM
# require(e1071)
# svmRule=best.tune('svm',
# train.x=x,
# train.y=factor(y),
# ranges=list(gamma=c(2^(-4:4),
# cost = 2^(-2:2))))
# for comparison with randomForest
require(randomForest)
RF <- best.tune('randomForest',x,factor(y),ranges=list(ntree = c(100,500)))
# for comparison with nearest chrunken centroid
#require(pamr)
#myTrainingdata=list(x=t(x),y=y)
#mytrain <- pamr.train(myTrainingdata)
#mycv <- pamr.cv(mytrain,myTrainingdata)
#thresh=try(mycv$threshold[which.min(mycv$error)],silent = TRUE)
#Testing Set
x=NULL; y=NULL;
for (k in 1:2){
M=matrix(rnorm(p*n),nrow=p,ncol=n)
x=rbind(x,t(array(C[,k]^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
y=c(y,array(k,n))
}
#Testing
myTestingdata=list(x=x,y=y)
QDAScore=mean((y!=predict(LearnedQuadBinaryRule,myTestingdata$x))) ;
LDAScore=mean((y!=predict(LearnedLinBinaryRule,myTestingdata$x))) ;
RFScore=mean((y!=predict(RF,myTestingdata$x))) ;
#SVMScore=mean((y!=predict(svmRule,x))) ;
#comparison with nearest chrunken centroid
myTestingdata=list(x=t(x),y=y)
#V=as.numeric(pamr.predict(mytrain, myTestingdata$x,threshold=thresh,type="class"))
#SCScore=mean((myTestingdata$y!=V))
cat('\n')
cat('What does it cost to use type=linear when the rule is quadratic ? ','\n',
'Score of the linear rule: ',LDAScore,'\n',
'Score of the quadratic rule: ',QDAScore,'\n',
#'Score of the nearest shrunken centroid rule: ',SCScore,'\n',
'Score of the random forest rule: ',RFScore,'\n',
#'Score of the support vector machine rule: ',SVMScore,'\n',
'Note: These scores should be average for a large number of experiment or interpreted carefully \n')
plotClassifRule(LearnedQuadBinaryRule)
############ Tests 2 classes quadratic and linear. when the true is linear
#library(VHDClassification)
#p=100; n=50 ; mu=array(0,c(p,2)); mu[1:10,1]=1 ;C=array(c(1,20),p)
#x=NULL; y=NULL;
#for (k in 1:2){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
#Learning
#LearnedQuadBinaryRule=learnBinaryRule(x,y,type='quadratic')
#LearnedLinBinaryRule=learnBinaryRule(x,y) # default is linear type
#comparison with nearest chrunken centroid
#require(pamr)
#myTrainingdata=list(x=t(x),y=y)
#mytrain <- pamr.train(myTrainingdata)
#mycv <- pamr.cv(mytrain,myTrainingdata)
#thresh=try(mycv$threshold[which.min(mycv$error)],silent = TRUE)
#Testing Set
#x=NULL; y=NULL;
#for (k in 1:2){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
#}
#Testing
#myTestingdata=list(x=x,y=y)
#QDAScore=mean((y!=predict(LearnedQuadBinaryRule,myTestingdata$x))) ;
#LDAScore=mean((y!=predict(LearnedLinBinaryRule,myTestingdata$x))) ;
#comparison with nearest shrunken centroid
#myTestingdata=list(x=t(x),y=y)
#tmp=as.numeric(pamr.predict(mytrain,threshold=thresh,
# myTestingdata$x,type="class"))
#SCScore=mean((myTestingdata$y!=tmp))
#cat('\n',
#'What does it cost to use type=
# quadratic rule when the true optimal rule is linear ? ','\n',
#'Score of the linear rule: ',LDAScore,'\n',
#'Score of the rule with type=quadratic : ',QDAScore,'\n',
# 'it detects that the true rule is linear?\n',
#'Score of the nearest shrunken centroid rule: ',SCScore,'\n')
#plotClassifRule(LearnedQuadBinaryRule)
############ Tests 3 classes
#library(VHDClassification)
#p=1000; n=40 ; mu=array(0,c(p,3)); mu[1:10,1]=4; C=array(c(1,20),p)
#x=NULL; y=NULL;
#for (k in 1:3){
# if (k<3){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
# else
# {
# tildeC=C; tildeC[1:10]=40;
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(tildeC^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
# }
# }
#Learning
#LearnedLinearPartitionWithLLR=learnPartitionWithLLR(x,y,type='linear')
#LearnedQuadraticPartitionWithLLR=learnPartitionWithLLR(x,y,type='quadratic')
#plotClassifRule(LearnedQuadraticPartitionWithLLR)
#require(randomForest)
#RF <- best.tune('randomForest',x,factor(y),ranges=list(ntree = c(500)))
#Testing Set
#x=NULL; y=NULL;
#for (k in 1:3){
# if (k<3){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
# else
# {
# tildeC=C; tildeC[1:10]=40;
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(tildeC^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
# }
# }
#Testing
#myTestingdata=list(x=x,y=y)
#LDAScore=mean((y!=factor(predict(LearnedLinearPartitionWithLLR,myTestingdata$x)))) ;
#QDAScore=mean((y!=factor(predict(LearnedQuadraticPartitionWithLLR,myTestingdata$x)))) ;
#RFScore=mean((y!=predict(RF,myTestingdata$x))) ;
#cat('Score of the quadratic rule: ',QDAScore,'\n',
#'Score of the linear rule: ',LDAScore,'\n',
#'Score of the random Forest Rule: ',RFScore,'\n')
VHDClassification documentation built on May 2, 2019, 2:38 a.m.
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Description Details Author(s) References Examples
Description
This package provides an implementation of Linear disciminant analysis and quadratic discriminant analysis that works fine in very high dimension (when there are many more variables than observations).
Details
| Package: | VHDClassification |
| Type: | Package |
| Version: | 0.1 |
| Date: | 2010-04-15 |
| License: | GPL-2 |
| LazyLoad: | yes |
| Depends: | methods, e1071, lattice, stats |
This package provides learning procedure for classification in very high dimension.
Binary learning is done with learnBinaryRule while K-class (K>=2) learning is done
with function learnPartitionWithLLR.
learnBinaryRule can return an object LinearRule-class or an object QuadraticRule-class depending
whether type='linear' or 'quadratic'.
learnPartitionWithLLR basically returns a set of binary rules which is represented by the class PartitionWithLLR-class.
The used procedure for the learning are described in the papers cited below. The
The method predict (predict-methods) is implemented for class LinearRule-class QuadraticRule-class learnPartitionWithLLR.
It predicts the class of a new observation.
Author(s)
Maintainer-author: Robin Girard <robin.girard@mines-paristech.fr>
References
Fast rate of convergence in high dimensional linear discriminant analysis. R. Girard To appear in Journal of Nonparametric Statistics.\ Very high dimensional discriminant analysis with thresholding estimation. R. Girard. Submitted.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 | ############ Tests 2 classes when the true rule should be quadratic
#library(VHDClassification)
p=500; n=50 ; mu=array(0,c(p,2)) ; C=array(c(1,20),c(p,2)); C[c(1,3,5),1]=40
x=NULL; y=NULL;
for (k in 1:2)
{
M=matrix(rnorm(p*n),nrow=p,ncol=n)
tmp=array(C[,k]^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))
x=rbind(x,t(tmp));
y=c(y,array(k,n))
}
#Learning
LearnedQuadBinaryRule=learnBinaryRule(x,y,type='quadratic')
LearnedLinBinaryRule=learnBinaryRule(x,y) # default is linear type
# for comparison with SVM
# require(e1071)
# svmRule=best.tune('svm',
# train.x=x,
# train.y=factor(y),
# ranges=list(gamma=c(2^(-4:4),
# cost = 2^(-2:2))))
# for comparison with randomForest
require(randomForest)
RF <- best.tune('randomForest',x,factor(y),ranges=list(ntree = c(100,500)))
# for comparison with nearest chrunken centroid
#require(pamr)
#myTrainingdata=list(x=t(x),y=y)
#mytrain <- pamr.train(myTrainingdata)
#mycv <- pamr.cv(mytrain,myTrainingdata)
#thresh=try(mycv$threshold[which.min(mycv$error)],silent = TRUE)
#Testing Set
x=NULL; y=NULL;
for (k in 1:2){
M=matrix(rnorm(p*n),nrow=p,ncol=n)
x=rbind(x,t(array(C[,k]^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
y=c(y,array(k,n))
}
#Testing
myTestingdata=list(x=x,y=y)
QDAScore=mean((y!=predict(LearnedQuadBinaryRule,myTestingdata$x))) ;
LDAScore=mean((y!=predict(LearnedLinBinaryRule,myTestingdata$x))) ;
RFScore=mean((y!=predict(RF,myTestingdata$x))) ;
#SVMScore=mean((y!=predict(svmRule,x))) ;
#comparison with nearest chrunken centroid
myTestingdata=list(x=t(x),y=y)
#V=as.numeric(pamr.predict(mytrain, myTestingdata$x,threshold=thresh,type="class"))
#SCScore=mean((myTestingdata$y!=V))
cat('\n')
cat('What does it cost to use type=linear when the rule is quadratic ? ','\n',
'Score of the linear rule: ',LDAScore,'\n',
'Score of the quadratic rule: ',QDAScore,'\n',
#'Score of the nearest shrunken centroid rule: ',SCScore,'\n',
'Score of the random forest rule: ',RFScore,'\n',
#'Score of the support vector machine rule: ',SVMScore,'\n',
'Note: These scores should be average for a large number of experiment or interpreted carefully \n')
plotClassifRule(LearnedQuadBinaryRule)
############ Tests 2 classes quadratic and linear. when the true is linear
#library(VHDClassification)
#p=100; n=50 ; mu=array(0,c(p,2)); mu[1:10,1]=1 ;C=array(c(1,20),p)
#x=NULL; y=NULL;
#for (k in 1:2){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
#Learning
#LearnedQuadBinaryRule=learnBinaryRule(x,y,type='quadratic')
#LearnedLinBinaryRule=learnBinaryRule(x,y) # default is linear type
#comparison with nearest chrunken centroid
#require(pamr)
#myTrainingdata=list(x=t(x),y=y)
#mytrain <- pamr.train(myTrainingdata)
#mycv <- pamr.cv(mytrain,myTrainingdata)
#thresh=try(mycv$threshold[which.min(mycv$error)],silent = TRUE)
#Testing Set
#x=NULL; y=NULL;
#for (k in 1:2){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
#}
#Testing
#myTestingdata=list(x=x,y=y)
#QDAScore=mean((y!=predict(LearnedQuadBinaryRule,myTestingdata$x))) ;
#LDAScore=mean((y!=predict(LearnedLinBinaryRule,myTestingdata$x))) ;
#comparison with nearest shrunken centroid
#myTestingdata=list(x=t(x),y=y)
#tmp=as.numeric(pamr.predict(mytrain,threshold=thresh,
# myTestingdata$x,type="class"))
#SCScore=mean((myTestingdata$y!=tmp))
#cat('\n',
#'What does it cost to use type=
# quadratic rule when the true optimal rule is linear ? ','\n',
#'Score of the linear rule: ',LDAScore,'\n',
#'Score of the rule with type=quadratic : ',QDAScore,'\n',
# 'it detects that the true rule is linear?\n',
#'Score of the nearest shrunken centroid rule: ',SCScore,'\n')
#plotClassifRule(LearnedQuadBinaryRule)
############ Tests 3 classes
#library(VHDClassification)
#p=1000; n=40 ; mu=array(0,c(p,3)); mu[1:10,1]=4; C=array(c(1,20),p)
#x=NULL; y=NULL;
#for (k in 1:3){
# if (k<3){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
# else
# {
# tildeC=C; tildeC[1:10]=40;
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(tildeC^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
# }
# }
#Learning
#LearnedLinearPartitionWithLLR=learnPartitionWithLLR(x,y,type='linear')
#LearnedQuadraticPartitionWithLLR=learnPartitionWithLLR(x,y,type='quadratic')
#plotClassifRule(LearnedQuadraticPartitionWithLLR)
#require(randomForest)
#RF <- best.tune('randomForest',x,factor(y),ranges=list(ntree = c(500)))
#Testing Set
#x=NULL; y=NULL;
#for (k in 1:3){
# if (k<3){
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(C^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))}
# else
# {
# tildeC=C; tildeC[1:10]=40;
# M=matrix(rnorm(p*n),nrow=p,ncol=n)
# x=rbind(x,t(array(tildeC^(1/2),c(p,n))*(M)+array(mu[,k],c(p,n))));
# y=c(y,array(k,n))
# }
# }
#Testing
#myTestingdata=list(x=x,y=y)
#LDAScore=mean((y!=factor(predict(LearnedLinearPartitionWithLLR,myTestingdata$x)))) ;
#QDAScore=mean((y!=factor(predict(LearnedQuadraticPartitionWithLLR,myTestingdata$x)))) ;
#RFScore=mean((y!=predict(RF,myTestingdata$x))) ;
#cat('Score of the quadratic rule: ',QDAScore,'\n',
#'Score of the linear rule: ',LDAScore,'\n',
#'Score of the random Forest Rule: ',RFScore,'\n')
|
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