Do not scale!
library(FactoMineR)data
cs <- cos((0:9)*pi/5)
sn <- sin((0:9)*pi/5)
er <- rnorm(10)/10
datcse <- cbind.data.frame(cs=cs, sn=sn, er=er)誤差なし
par(mar=c(2.5,2.5,2,0.3), mgp=c(1.5, 0.5, 0), mfrow=c(1,1))
res0 <- PCA(datcse[,1:2], scale.unit=FALSE)
多少の誤差は、標準化しなければわずかな影響
rescsen <- PCA(datcse, scale.unit=FALSE)
標準化すると、恐ろしい結果が
rescse <- PCA(datcse)
誤差がさらにあると、さらにひどい事態に
datcse2 <- cbind.data.frame(cs=cs, sn=sn, er=er, er2 = runif(10)/10)
PCA(datcse2)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 10 individuals, described by 4 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"さらに増えると、尤もらしい最悪な事態に
datcse4 <- cbind.data.frame(cs=cs, sn=sn, er=er, er2 = runif(10)/10, er3=rnorm(10)/10, er4=rpois(10,1)/10)
PCA(datcse4)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 10 individuals, described by 6 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"それでも 標準化しなければ大丈夫
PCA(datcse4, scale.unit = FALSE)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 10 individuals, described by 6 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"もう一つの例
sin curve を垂直方向に微妙に 誤差があるものを、PCA 処理を おこなう。 not scaled では、本来の図が 復元される。しかし scaled の 場合は、とんでもない図になる。 つまり、誤差が針小棒大となり 崩れてしまう。
なお、曲線のデータではなく、 201点のデータである。
par(mar=c(2.5,2.5,2,0.3), mgp=c(1.5, 0.5, 0), mfrow=c(1,1))
xpts <- 2*(-100:100)/100
ysin <- sin(xpts * pi)
plot(xpts, ysin, type="l", asp=1, main="original 2-dim data")
ecos <- 0.01*cos(xpts * pi)
plot(xpts, ecos, type="l", asp=1, main="1-3 dim")
dat2 <- cbind.data.frame(xpts, ysin, ecos)
suf <- PCA(dat2, scale.unit=F, graph=FALSE)
plot(suf, choix="var", title="Not Scaled PCA")
plot(suf$ind$coord, type="l", main="Not Scaled PCA")
sut <- PCA(dat2, scale.unit=T, graph=FALSE)
plot(sut, choix="var", title="Scaled PCA")
plot(sut$ind$coord, type="l", main="Scaled PCA")