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Assume that you have a matrix $X$ and you want to project it onto a subspace by using PCA. It will work. Then you are trying to use a linear autoencoder to projecting $X$ onto the same subspace. It will work too.

Question:

Assume that the PCA projection has $c$ components. Can a linear autoencoder project $X$ onto the subspace with the same results as PCA does, with layers $l$ that are less then components $c$?

My goal here is to create a linear autoencoder that can perform the same results, with less layers than components.

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  • $\begingroup$ If I am understanding correctly, it would seem that you would need the dimension of the subspace to be equal to both $c$ and $l$, so that $c$ and $l$ would have to be equal. $\endgroup$
    – Steven Gubkin
    Commented Jul 25, 2023 at 21:33
  • $\begingroup$ @StevenGubkin More like if a linear AE with fewer layers, can do the same as regular PCA with more components. $\endgroup$
    – euraad
    Commented Jul 26, 2023 at 12:05

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