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I have to do canonical correlation analysis between two multivariate datasets X and Y. One dataset contain numerical data and the other binary data. I would like to know what features are highly correlated with the features in second data set.

  1. Would the normal CCA available in MATLAB be sufficient if one data set has numerical (integer and floating point values) and the second dataset has binary values (0 or 1) for all the values for the various features?
  2. How to tackle this problem if both data sets are composed of binary variables?
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    $\begingroup$ It is OK to use standard CCA with data which partly or all are binary variables. Since a binary variable has only two levels, if behaves identically whether it is seen as numeric or categorical. At least with analyses based on correlations - such as CCA. $\endgroup$
    – ttnphns
    Commented Jan 19, 2014 at 18:22
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    $\begingroup$ However, if you prefer to think that your canonical variates are like latent factors, there is a theoretical stumbling block, because, logically, you can't extract continuous latent trait out of truly categorical data. You have to admit that the data are discretized continuous, which opens complex question whether an inferred correlation (such as tetrachoric) should be used in place of the observed one (Pearson r). $\endgroup$
    – ttnphns
    Commented Jan 19, 2014 at 18:46
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    $\begingroup$ @ttnphns, why not make that an official answer? $\endgroup$
    – gung - Reinstate Monica
    Commented Jan 19, 2014 at 20:25

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From ttnphns comment:

It is OK to use standard CCA with data which partly or all are binary variables. Since a binary variable has only two levels, if behaves identically whether it is seen as numeric or categorical. At least with analyses based on correlations - such as CCA

In addition: if one has other categorical variables (with more than 2 categories) is also fine to convert them to dummy variables (after removing one to avoid redundancy). Problems might come when needed to interpret the results tough.

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  • $\begingroup$ Mean squared canonical correlation of such analysis will be equal to the squared Cramer's V assosiation between the two categorical variables. $\endgroup$
    – ttnphns
    Commented Oct 18, 2018 at 16:21

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