monogenea

houses <- read.table("http://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data",
                     header = F, na.string = "?")
colnames(houses) <- c("CRIM", "ZN", "INDUS","CHAS",
                      "NOX","RM","AGE","DIS","RAD",
                      "TAX","PTRATIO","B","LSTAT","MEDV")

# Perform PCA
pcaHouses <- prcomp(scale(houses[,-14]))
scoresHouses <- pcaHouses$x

monogenea

str(winePCAmethods) # slots are marked with @
winePCAmethods@R2

monogenea

winePCAmethods <- pca(wine[,-1], scale = "uv", center = T,
                      nPcs = 2, method = "svd")
slplot(winePCAmethods, scoresLoadings = c(T,T),
       scol = wineClasses)

monogenea

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install("pcaMethods")
library(pcaMethods)

monogenea

wineOutlier <- wine
wineOutlier[10,] <- wineOutlier[10,]*10 # change the 10th obs. into an extreme one by multiplying its profile by 10
outlierPCA <- prcomp(scale(wineOutlier[,-1]))
plot(outlierPCA$x[,1:2], col = wineClasses)

monogenea

dev.off() # clear the format from the previous plot
winePCA <- prcomp(scale(wine[,-1]))
plot(winePCA$x[,1:2], col = wineClasses)

monogenea

# Name the variables
colnames(wine) <- c("Cvs","Alcohol","Malic acid","Ash",
                    "Alcalinity of ash", "Magnesium",
                    "Total phenols", "Flavanoids",
                    "Nonflavanoid phenols", "Proanthocyanins",
                    "Color intensity", "Hue",
                    "OD280/OD315 of diluted wines", "Proline")

# The first column corresponds to the classes
wineClasses <- factor(wine$Cvs)

monogenea

wine <- read.table("http://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data",
                   sep=",")

monogenea

# Compare PCA scores with the SVD's U*Sigma
theoreticalScores <- mySVD$u %*% sigma
all(round(myPCA$x,5) == round(theoreticalScores,5)) # TRUE

# Compare PCA loadings with the SVD's V
all(round(myPCA$rotation,5) == round(mySVD$v,5)) # TRUE

# Show that mat == U*Sigma*t(V)
recoverMatSVD <- theoreticalScores %*% t(mySVD$v)
all(round(mat,5) == round(recoverMatSVD,5)) # TRUE

monogenea

# Perform SVD
mySVD <- svd(mat)
mySVD # the diagonal of Sigma mySVD$d is given as a vector
sigma <- matrix(0,4,4) # we have 4 PCs, no need for a 5th column
diag(sigma) <- mySVD$d # sigma is now our true sigma matrix