correspondence analysis

以下サイトを参考にしました。二つ目のコードです。（URL：https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Correspondence_Analysis.pdf ）

library(dplyr)

n=10

data=data.frame(n1=c(rpois(n/2,lambda=5),rpois(n/2,lambda=10)),n2=rpois(n,5),n3=rpois(n,8),n4=rpois(n,12))

ave_col=apply(data,2,sum);ave_row=apply(data,1,sum)

c_ij=(as.matrix(data)-mean(ave_col)[1])/sqrt(mean(ave_col)/sum(ave_col))

mat=array(0,dim=c(nrow(data),ncol(data)))

for(i in 1:nrow(data)){
for(j in 1:ncol(data)){

mat[i,j]=(ifelse(i==j,1,0)-mean(ave_col)[1]/sum(ave_col))/sqrt(mean(ave_col)/sum(ave_col))

}
}  

eigen(cor(c_ij))

eigen(cor(mat))

#correspondence analysis

library(dplyr)

n=10

data=data.frame(n1=c(rpois(n/2,lambda=5),rpois(n/2,lambda=10)),n2=rpois(n,5),n3=rpois(n,8),n4=rpois(n,12))

K=as.matrix(data)

P=K/sum(K);c=apply(P,2,sum);r=apply(P,1,sum)

D_r=sqrt(solve(diag(r)))

D_c=sqrt(solve(diag(c)))

A=D_r%*%P%*%D_c

mat=svd(A)

B=mat$u;W=diag(mat$d);C=mat$v

f=D_r%*%B%*%W

g=D_c%*%C%*%W

V=(W%*%W)

eigen_values=diag(V)

row_d=c();col_d=c()

for(i in 1:nrow(P)){

row_d=c(row_d,sum((P[i,]/apply(P,1,sum)[i]-apply(P,2,sum))^2/apply(P,2,sum)) ) 

}

for(j in 1:ncol(P)){

col_d=c(col_d,sum((P[,j]/apply(P,2,sum)[j]-apply(P,1,sum))^2/apply(P,1,sum)))  

}

Inertia_r=r*row_d^2/sum((r*row_d)^2)

Inertia_c=c*col_d^2/sum((c*col_d)^2)

row_d^2

col_d^2