Reconstruct low dimensional PCA projection

Question

Suppose I have high dimensional data (say 32 dimension) and I projected the data onto 2D space. How can I project (or approximate) these 2 dimensional point back onto the original 32 dimensions. \
In particular, I wish to approximate any random point in 2D to the original space. Explanation through python code is much appreciated.

Answer 1

You can direct do that in sklearn with inverse_transform().

from sklearn.decomposition import PCA
import numpy as np
X=np.random.rand(100,32)

pca = PCA(n_components=2)
pca.fit(X)
X_reduced=pca.transform(X)


X_inverse=pca.inverse_transform(X_reduced)

Trying with random arrays you see that the operation is not biunivocal because it not necessary produce the original X input.

But if you try to reduce the "inverse" X:

X_inv_red=pca.transform(X_inverse)

You get the same PCA reduction as the original X input.

You can use it in whatever 2D point.

inverse_transform()