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What are the cases when we should not use PCA for dimensionality reduction and what to use in such cases?

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    $\begingroup$ Use PCA when it gets better results, or for visualizations.. $\endgroup$ – Hobbes Jun 26 '17 at 20:32
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You should not use PCA if you only have categorical variables, and thus the distance function in PCA is invalid.

Correspondence analysis is a common alternative.

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PCA is a linear transformation of your variables to a set of uncorrelated ones.

It is good when you want to remove redundancy (in a linear sense) in your data but it is bad if you want to uncover the "true cause" of the variables. Furthermore the causes can be non-linear in nature and the behavior of your data cannot be captured using a linear model.

Then you would stay away from PCA and consider e.g. non linear dimensionality reduction methods

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