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I having binary data set (yes/no), so can I apply PCA on that. Is it mathematically correct to do that. In my opinion Binary variable can only be subjected to logical operations, so how it can be legal to apply PCA on the binary varaibles . Previously Question similar questions have been asked Doing principal component analysis or factor analysis on binary data (using SPSS) but I could not clear my doubt.

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I agree with you that whilst PCA is mathematical correct it however seems less appropriate on non - continuous data. I had a similar doubt and googling around I found an R-Bloggers post about Homogeneity Analysis that deals with the same problem and offer a solution. http://www.r-bloggers.com/finding-patterns-amongst-binary-variables-with-the-homals-package/

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    $\begingroup$ I think that would a senseless swop. HOMALS (aka Multiple Correspondence analysis) is - as far as I know - equivalent to usual PCA when all the variables are dichotomous. $\endgroup$
    – ttnphns
    Jun 19, 2014 at 14:45

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