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I have read about auto-encoders and RBMs being used to perform non-linear PCA by forcing the hidden layers to learn a good representation of the input features with reduced dimensions. But how do these networks actually find the principal components with the maximum variance which is what PCA is supposed to do?

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The RBM and auto-encoders algorithms do not reduce dimension in a way that maximizes the variance. They don't have such a property.

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