What is the intuition behind number 1 and 2 when it comes to considering mean? And how will this affect performance and accuracy?
Number 1:
pca = decomposition.PCA(n_components=4)
X_centered = X - X.mean(axis=0)
pca.fit(X_centered)
X_pca = pca.transform(X_centered)
Number 2:
pca = decomposition.PCA(n_components=4)
pca.fit(X)
X_pca = pca.transform(X)
Thanks in advance
It will be the same. In a way, PCA find a set of basis vectors, which are orthogonal to each and maximize the variance in a set of points projections onto them. PCA therefore has rotation and translation symmetry. Therefore you will have identical PCA results whenever you shift your matrix (which is what subtraction of the mean essentially does) to not.
If some variables have a large variance and some small, PCA (maximizing variance) will load on the large variances. For example, if you change one variable from km to cm (increasing its variance), it may go from having a little impact to dominating the first principle component. If you want your PCA to be independent of such rescaling, standardizing the variables will do that. On the other hand, if the specific scale of your variables matters (in that you want your PCA to be on that scale), maybe you don't want to standardize.