PCA：如何获得指向新坐标系原点的向量？

Question

PCA将原始数据点投影到新的坐标系中，我想确定将旧坐标系的原点与R中新坐标系的原点相连的向量。

这是我到目前为止所编码的内容：

data <- data.frame(cbind(c(5,15,21,29,31,43,49,51,61,65),
c(33,35,24,21,27,16,18,10,4,12)))


# Subtract columns by their mean and 
# divide with their standard deviation
scaled_data <- scale(data, center=TRUE, scale=TRUE)
scaled_data
plot(scaled_data)

# Correlation Matrix
corrmat <- cor(scaled_data)
corrmat

# Compute Eigenvalues and Eigenvectors
eigen <- eigen(corrmat)

eigenvectors <- eigen$vectors
eigenvectors

eigenvalues <- eigen$values
eigenvalues

# Transform data
transformed_data <- (data.matrix(scaled_data) %*% eigenvectors)*sqrt(2)
transformed_data

plot(transformed_data)

Answer 1

新坐标系的起源是数据集的重心（a.k.a.质心）：

colMeans(data)
# X1 X2 
# 37 20