2. In this problem we will perform principal component analysis on the sepal and

Question

2. In this problem we will perform principal component analysis on the sepal and petal measurements of the first 50 flowers in the Iris data, i.e., iris[1:50,1:4] (a) Center the data matrix and denote the centered data matrix by X. Find the covari ance matrix Sx of X (b) Report the eigenvectors of Sx and the variance of X along each eigenvector direction. (c) Calculate the principal components of the first two flowers. (d) Make a scatter plot of the first two principal components of the data. Do you see any correlation between the two principal components? (e) If we wish to keep at least 85% of the total variance, how many principal components do we need to keep?

Explanation / Answer

data("iris")
dim(iris)
new_iris<-iris[1:50,1:4]
dim(new_iris)
View(new_iris)
##a###
# center with 'colMeans()'
centerColMean <- function(x) {
xcenter = colMeans(x)
x - rep(xcenter, rep.int(nrow(x), ncol(x)))
}

# apply it
X<-centerColMean(new_iris)
View(X)

#Correlation Matrix
Sx<-cor(X)
View(Sx)
#____________________________________________________________

##b##

X<-as.matrix(X)
Sx<-as.matrix(Sx)

X_eigen<-eigen(Sx)
X_eigen

#eigen vectors of Sx
X_eigen$vectors

'''
The eigenvector with the largest eigenvalue is the direction along which the data
set has the maximum variance.
'''
X_eigen$values[1]*X_eigen$vectors
X_eigen$values[2]*X_eigen$vectors
X_eigen$values[3]*X_eigen$vectors
X_eigen$values[4]*X_eigen$vectors
#______________________________________________________________________________

##c##

pca<-prcomp(X[1:2,1:4])
pca

plot(pca)

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.