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I have a data set where one of the variables is in polar coordinates ($\varphi$ = 0° to 360° degrees) and PCA was applied in order to reduce dimensions.

As far as I know, using PCA on polar coordinates does not make sense from a mathematical point of view, because 0° and 360° would be treated as completely opposite values, although being essentially the same (am I right?)

What would be the optimal approach to using PCA on such a data set with mixed types of variables including polar coordinates?

What I thought of is transforming polar coordinates to Cartesian coordinates (assuming $r = 1$): $x = cos \varphi$ and $y = sin \varphi$ and weighting these new variables by 0.5. Is this solution mathematically correct? Are there any other suggestions to solve this?

knytt
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    PCA, as an exploratory and descriptive method, cannot readily be evaluated on the basis of "mathematical correctness." If what you are doing is interpretable and insightful (both of which seem to be the case), then there should be nothing to complain about. – whuber May 11 '20 at 21:20
  • Similar question: https://stats.stackexchange.com/questions/338885/pca-on-polar-coordinates – Ron Jensen May 11 '20 at 21:54

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