使用 SKLearn 和 Python 的 PCA - 使用给定的分量/基向量计算 PCA 值

Question

I'm trying to understand what sklearn is doing when running a PCA . Unfortunately I don't have much knowledge with PCA so it might be my understand is just wrong.

Let's have a simple example with the iris dataset:

iris = datasets.load_iris()
X = iris.data
pca.fit(X)
Xfit = pca.transform(X)

Xfit now looks like this:

[[-2.68412563e+00,  3.19397247e-01, -2.79148276e-02, -2.26243707e-03], ...

I thought that to get these projected values I basically just need to build the dot product of the original values and the transposed basic vectors / components . So I assumed that this should give the same result:

np.dot(X, np.transpose(pca.components_))

But unfortunately this is the result:

[[ 2.81823951e+00,  5.64634982e+00, -6.59767544e-01, 3.10892758e-02],..

So my question is:

Why is there a difference? I asume the one from pca.transform(X) is correct and I'm doing something wrong but what would I need to do if I only have the components and would like to calculate the principal component values myselfs?

Answer 1

Alright, I've found the issue. I have to mean-center the raw values before applying np.dot . So when using only pd.DataFrame , which makes mean-centering pretty easy, it looks like this:

np.dot(pd.DataFrame(X)-pd.DataFrame(X).mean(), np.transpose(pd.DataFrame(pca.components_)))

and the results are the same as when using the fit function:

[[-2.68412563e+00,  3.19397247e-01, -2.79148276e-02, -2.26243707e-03], ...