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As the title states: PCA is an autoencoder with one hidden layer with linear transfer functions.

Can someone explain this sentence to me? I understand that if you want to map something into lower dimensional space then PCA has essentially perfectly optimized this procedure. With this understanding, if an autoencoder has a loss function that aims to find the best representation in lower dimensional space (say dimension H) then PCA that takes H rank basis vectors will produce the exact same result as the autoencoder?

Which of these is quicker and a better approach?

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  • $\begingroup$ Take a look at: stats.stackexchange.com/questions/120080/… $\endgroup$ – Hossein Mar 30 '17 at 17:19
  • $\begingroup$ @Hossein Hey, thanks for your response. That doesn't really tell me about the process only that they get to the same result. I'm curious about how they get to that result since my book just says that "what an autoencoder does is the same as getting the SVD and getting rank H" $\endgroup$ – tryingtolearn Mar 30 '17 at 20:14