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# File: ReadMe.txt
# Aim : A brief introduction about the usage for Chen songxi's method and Chen songxi's method under Gauss Kernel
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# Author: Yuan Huili (Peking University)
# Email : hlyuan@pku.edu.cn
# Date  : 05/29/2015
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# Files needed: 
#               SXvsKerSX.R
# Function parameter description:
#   function: SXCHEN
#   input:
#          n1 ------ the number of samples in class 1
#          n2 ------ the number of samples in class 2
#          X1 ------ n1xp data matrix, row is sample, col is variable
#          X2 ------ n2xp data matrix, row is sample, col is variable    
#   output: a numeric value
#          SXCHEN--- the difference of two covariance matrices under Frobenius norm
#   function: GSXCHEN
#   input:
#          n1 ------ the number of samples in class 1
#          n2 ------ the number of samples in class 2
#          X1 ------ n1xp data matrix, row is sample, col is variable
#          X2 ------ n2xp data matrix, row is sample, col is variable
#        coef ------ the parameter in Gauss kernel   
#   output: a numeric value
#          GSXCHEN--- the difference of two covariance operators under Hilbert-Schmidt norm
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# Basic example
# 
source("SXvsKerSX.R");
# 1. generate two classes of samples
generate<-function(theta,m,p)
{
Z<-matrix(0,nrow=m,ncol=p)
for(j in 1:m)
{
  for(k in 1:p)
  {
   Z[j,k]<-rnorm(1,0,1)
  }
}
X<-matrix(0,nrow=m,ncol=p)
for(j in 1:m)
{
  for(k in 1:(p-1))
  {
   X[j,k]<-exp(Z[j,k])*theta*exp(Z[j,k+1])
  }
   X[j,p]<-exp(Z[j,p])*theta*exp(Z[j,1])
}
generate<-X
}
m<-50
n<-50
p<-50
threshold<-0.1
library(MASS)
X<-generate(0.5,m,p)
Y<-generate(0.2,m,p)
# 2. run SXCHEN
sxchen<-SXCHEN(m,n,t(X),t(Y))
# 3. run GSXCHEN
gsxchen<-GSXCHEN(m,n,t(X),t(Y),10)
# 4.
if(sxchen>threshold)
print("The two covariance matrices are different under Frobenius norm.")
if(sxchen<=threshold)
print("The two covariance matrices are the same under Frobenius norm.")
if(gsxchen>threshold)
print("The two covariance operators are different under Hilbert-Schmidt norm.")
if(gsxchen<=threshold)
print("The two covariance operators are the same under Hilbert-Schmidt norm.")
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