PCA scaling and centering documentation wrong?

8 Ansichten (letzte 30 Tage)
Ari Paul
Ari Paul am 24 Mär. 2015
Bearbeitet: the cyclist am 8 Aug. 2022
The pca() documentation says that the raw data is automatically centered at the start of the process. If true, then pca(X) should be equal to pca(Y), where Y = centered data. But they're not (specific data below). Additionally, when I use either eig() or svd() to compute the principal components, I can only get them to match the pca output when I first manually center the data before using pca(). Ultimately my question is simply how do I correctly calculate the principal components of raw data? I.e. do I need to manually center and scale it first? Only manually center? Only manually scale?
Sample data: X =
1.0000 -3.0000 -1.0000; 2.0000 -2.0000 -0.5000; 3.0000 -0.5000 0.2500; 4.0000 2.0000 1.0000; 5.0000 5.0000 2.5000;
Centering X -> Y= -2.0000 -3.3000 -1.4500; -1.0000 -2.3000 -0.9500; 0 -0.8000 -0.2000; 1.0000 1.7000 0.5500; 2.0000 4.7000 2.0500;
pca(X) = -0.7360 -0.6037 -0.3062; -0.6688 0.7186 0.1907; -0.1049 -0.3452 0.9327;
pca(Y) =
0.4058 0.8414 0.3569
0.9124 -0.3960 -0.1036
0.0542 0.3676 -0.9284
svd(Y) = 0.4058 0.9124 0.0542; 0.8414 -0.3960 0.3676; 0.3569 -0.1036 -0.9284;
eig(cov(Y)) = 0.0542 0.9124 0.4058; 0.3676 -0.3960 0.8414; -0.9284 -0.1036 0.3569; ^this is the same output just in a different order.

Antworten (2)

Sagar
Sagar am 9 Aug. 2015
You got it little wrong. When you do PCA(Y), by default, PCA again centers the data. So if you want to get the same values as PCA(X), use 'centered', 'off' name-value pair option: PCA_of_Y = PCA (Y, 'centered', 'off'); Now it will definitely be equal to PCA(X).

the cyclist
the cyclist am 26 Jun. 2019
Bearbeitet: the cyclist am 8 Aug. 2022
Answering a gazillion years after-the-fact, because I just turned this up in my own search.
X = [1.0000 -3.0000 -1.0000;
2.0000 -2.0000 -0.5000;
3.0000 -0.5000 0.2500;
4.0000 2.0000 1.0000;
5.0000 5.0000 2.5000];
Y = X - mean(X);
pca(X)
ans = 3×3
0.4058 0.9124 -0.0542 0.8414 -0.3960 -0.3676 0.3569 -0.1036 0.9284
pca(Y)
ans = 3×3
0.4058 0.9124 -0.0542 0.8414 -0.3960 -0.3676 0.3569 -0.1036 0.9284
both give the same PCA results (as of when I answered this).
So, either something got fixed, or you made a mistake.

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