Conflicting Results When Manually Calculating First Principal Component using prcomp
I am calculating the PCA for the iris dataset as follows:
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
This is the first row of the iris dataset:
head(iris, 1)
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#1 5.1 3.5 1.4 0.2 setosa
For the first row, I can see that the value of the first principal component is -2.257141:
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751
But when I try extract the loadings:
ir.pca$rotation[, 1]
Sepal.Length Sepal.Width Petal.Length Petal.Width
0.5210659 -0.2693474 0.5804131 0.5648565
and calculate the first principal component myself:
0.5210659 * 5.1 + -0.2693474 * 3.5 + 0.5804131 * 1.4 + 0.5648565 * 0.2
I get a different result of 2.64027.
Why is that?
r pca predict
edited Jan 3 at 14:22
AkselA
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
add a comment |
I am calculating the PCA for the iris dataset as follows:
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
This is the first row of the iris dataset:
head(iris, 1)
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#1 5.1 3.5 1.4 0.2 setosa
For the first row, I can see that the value of the first principal component is -2.257141:
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751
But when I try extract the loadings:
ir.pca$rotation[, 1]
Sepal.Length Sepal.Width Petal.Length Petal.Width
0.5210659 -0.2693474 0.5804131 0.5648565
and calculate the first principal component myself:
0.5210659 * 5.1 + -0.2693474 * 3.5 + 0.5804131 * 1.4 + 0.5648565 * 0.2
I get a different result of 2.64027.
Why is that?
r pca predict
edited Jan 3 at 14:22
AkselA
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
add a comment |
I am calculating the PCA for the iris dataset as follows:
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
This is the first row of the iris dataset:
head(iris, 1)
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#1 5.1 3.5 1.4 0.2 setosa
For the first row, I can see that the value of the first principal component is -2.257141:
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751
But when I try extract the loadings:
ir.pca$rotation[, 1]
Sepal.Length Sepal.Width Petal.Length Petal.Width
0.5210659 -0.2693474 0.5804131 0.5648565
and calculate the first principal component myself:
0.5210659 * 5.1 + -0.2693474 * 3.5 + 0.5804131 * 1.4 + 0.5648565 * 0.2
I get a different result of 2.64027.
Why is that?
r pca predict
edited Jan 3 at 14:22
AkselA
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
I am calculating the PCA for the iris dataset as follows:
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
This is the first row of the iris dataset:
head(iris, 1)
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#1 5.1 3.5 1.4 0.2 setosa
For the first row, I can see that the value of the first principal component is -2.257141:
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751
But when I try extract the loadings:
ir.pca$rotation[, 1]
Sepal.Length Sepal.Width Petal.Length Petal.Width
0.5210659 -0.2693474 0.5804131 0.5648565
and calculate the first principal component myself:
0.5210659 * 5.1 + -0.2693474 * 3.5 + 0.5804131 * 1.4 + 0.5648565 * 0.2
I get a different result of 2.64027.
Why is that?
r pca predict
r pca predict
edited Jan 3 at 14:22
AkselA
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
edited Jan 3 at 14:22
AkselA
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
edited Jan 3 at 14:22
AkselA
4,66921326
edited Jan 3 at 14:22
AkselA
4,66921326
edited Jan 3 at 14:22
AkselA
4,66921326
4,66921326
asked Jan 3 at 13:43
orrymrorrymr
532824
asked Jan 3 at 13:43
orrymrorrymr
532824
asked Jan 3 at 13:43
orrymrorrymr
532824
532824
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Scaling is the issue.
Either drop scaling in the prcomp() call
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
# 1
# [1,] -5.912747
Or scale iris before you manually apply the loadings
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
# [,1]
# [1,] -2.257141
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Scaling is the issue.
Either drop scaling in the prcomp() call
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
# 1
# [1,] -5.912747
Or scale iris before you manually apply the loadings
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
# [,1]
# [1,] -2.257141
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
add a comment |
Scaling is the issue.
Either drop scaling in the prcomp() call
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
# 1
# [1,] -5.912747
Or scale iris before you manually apply the loadings
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
# [,1]
# [1,] -2.257141
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
add a comment |
Scaling is the issue.
Either drop scaling in the prcomp() call
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
# 1
# [1,] -5.912747
Or scale iris before you manually apply the loadings
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
# [,1]
# [1,] -2.257141
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
Scaling is the issue.
Either drop scaling in the prcomp() call
data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
# 1
# [1,] -5.912747
Or scale iris before you manually apply the loadings
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
head(ir.pca$x, 1)
# PC1 PC2 PC3 PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
# [,1]
# [1,] -2.257141
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
answered Jan 3 at 14:17
AkselAAkselA
4,66921326
4,66921326
add a comment |
add a comment |
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