#FCM2 p.36
#エントロピー関数による正則化
data(iris)
n=150;c=3
X=iris[,!(colnames(iris) %in% "Species")]
X=matrix(unlist(X),nrow=nrow(X),ncol=ncol(X))*10
class=unique(iris$Species)
lam=0.1
ite=1000
uik=array(1,dim=c(n,c))
uik=matrix(sample(c(1:9),n*c,replace=T)/10,nrow=n)
for(l in 1:ite){
v=array(0,dim=c(length(class),ncol(X)))
for(j in 1:c){
x=X
vec=apply(x*c(uik[,j]),2,sum)/sum(uik[,j])
v[j,]=vec
}
values=array(0,dim=dim(uik))
for(j in 1:c){
uik[,j]=exp(-lam*apply((t(t(X)-c(v[j,])))^2,1,sum))
values[,j]=apply((t(t(X)-c(v[j,])))^2,1,sum)
}
uik=uik/apply(uik,1,sum)
J=sum(uik*values)+sum(uik*log(uik))/lam
print(J)
}
#FCM2 p.39
#2次正則化
#試行中
data(iris)
n=150;c=4
X=iris[,!(colnames(iris) %in% "Species")]
X=matrix(unlist(X),nrow=nrow(X),ncol=ncol(X))*10
class=unique(iris$Species)
lam=10^(-0)
ite=50
uik=array(1,dim=c(n,c))
uik=matrix(sample(c(1:9),n*c,replace=T)/10,nrow=n)
for(l in 1:ite){
v=array(0,dim=c(c,ncol(X)))
for(j in 1:c){
x=X
vec=apply(x*c(uik[,j]),2,sum)/sum(uik[,j])
v[j,]=vec
}
values=array(0,dim=dim(uik))
for(j in 1:c){
values[,j]=apply((t(t(X)-c(v[j,])))^2,1,sum)
}
f=array(0,dim=dim(uik))
for(j in 1:c){
f[,j]=1+lam*(apply(values,1,sum)-c*values[,j])
}
uik=array(0,dim=dim(uik))
for(j in 1:c){
uik[,j]=(apply(ifelse(f>0,1,0)*values,1,sum)*lam+1)/apply(ifelse(f>0,1,0),1,sum)-lam*values[,j]
}
uik=ifelse(uik>0,uik,0)
J=sum(uik*values)+sum(uik^2)/(2*lam)
print(J)
}
#ファジィｃ多様体法 p.46
data(iris)
n=150;c=3
X=iris[,!(colnames(iris) %in% "Species")]
X=matrix(unlist(X),nrow=nrow(X),ncol=ncol(X))*10
class=unique(iris$Species)
Y=as.integer(iris$Species)*10
ite=100
uik=matrix(sample(c(1:9),n*c,replace=T)/10,nrow=n)
m=2;q=3
for(l in 1:ite){
w=array(0,dim=c(length(class),ncol(X)))
for(j in 1:c){
x=X
vec=apply(x*c(uik[,j]^m),2,sum)/sum(uik[,j]^m)
w[j,]=vec
}
Dik=array(0,dim=c(c,n))
for(j in 1:c){
A=array(0,dim=c(ncol(X),ncol(X)))
for(i in 1:nrow(X)){
A=A+(uik[i,j]^m)*t(t(c(X[i,]-w[j])))%*%t(c(X[i,]-w[j]))
}
s=eigen(A)$vectors[,1:q]
Dik[j,]=apply(t(t(X)-c(w[j,]))^2,1,sum)-apply((t(t(X)-c(w[j,]))%*%s)^2,1,sum)
}
for(j in 1:c){
sub=(t(1/Dik)*c(Dik[j,]))^(1/(m-1))
sub=apply(sub,1,sum)^(-1)
uik[,j]=sub
}
J=sum(t(Dik)*uik^m)
print(J)
}
#ファジィｃ回帰法 p.48
data(iris)
n=150;c=3
X=iris[,!(colnames(iris) %in% "Species")]
X=matrix(unlist(X),nrow=nrow(X),ncol=ncol(X))*10
class=unique(iris$Species)
Y=as.integer(iris$Species)*10
ite=100
uik=matrix(sample(c(1:9),n*c,replace=T)/10,nrow=n)
beta=array(1,dim=c(c,ncol(X)+1))
m=2
for(l in 1:ite){
Dik=array(0,dim=c(c,n))
for(j in 1:c){
Z=cbind(rep(1,nrow(X)),X)
b=solve(t(Z)%*%diag(c(uik[,j]))%*%Z)%*%t(Z)%*%diag(c(uik[,j]))%*%Y
beta[j,]=b
Dik[j,]=(Y-Z%*%b)^2
}
for(j in 1:c){
sub=(t(1/Dik)*c(Dik[j,]))^(1/(m-1))
sub=apply(sub,1,sum)^(-1)
uik[,j]=sub
}
J=sum(t(Dik)*uik^m)
print(J)
}
#5.3 非類似度を用いたファジィクラスタリング p.72
mat=matrix(0,nrow=10,ncol=10)
mat[1,]=c(0,8.89,10.16,15.84,16.84,33.01,32.69,43.47,37.78,39.31)
mat[2,]=c(0,0,9.64,15.37,20.45,30.75,34.09,41.61,39.26,41.47)
mat[3,]=c(0,0,0,6.12,11.2,22.98,24.56,33.61,29.75,31.86)
mat[4,]=c(0,0,0,0,8.48,17.20,18.75,27.64,23.91,26.23)
mat[5,]=c(0,0,0,0,0,20.77,16.25,29.52,21.17,22.49)
mat[6,]=c(0,0,0,0,0,0,13.01,10.86,15.61,19.06)
mat[7,]=c(0,0,0,0,0,0,0,15.99,5.19,7.69)
mat[8,]=c(rep(0,8),14.84,17.68)
mat[9,]=c(rep(0,9),3.45)
mat=mat+t(mat)
d=mat
c=3
uij=matrix(sample(1:9,c*nrow(d),replace=T),nrow=c)
w=0.1
eta=0.001
ite=10
for(l in 1:ite){
w_pre=w
uij_pre=uij
for(j in 1:c){
u_vec=uij[j,]
for(i in 1:ncol(uij)){
uij[j,i]=uij[j,i]-eta*sum((u_vec[i]-u_vec)*w*(w*(u_vec[i]-u_vec)^2-d[i,]))
}
}
du1=array(0,dim=c(ncol(uij),ncol(uij)))
du2=array(0,dim=c(ncol(uij),ncol(uij)))
for(j in 1:c){
u_vec=uij[j,]
du1=du1+d*(t(matrix(rep(u_vec,length(u_vec)),ncol=length(u_vec)))-u_vec)^2
du2=du2+(t(matrix(rep(u_vec,length(u_vec)),ncol=length(u_vec)))-u_vec)^4
}
w=sum(du1)/sum(du2)
cost=sum((uij-uij_pre)^2)+(w-w_pre)^2
print(cost)
}