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I label couples of similar and dissimilar instances based on user behavior. each instance has a lot of features. I have few ways of labeling the couples. I know want to evaluate which of the label methods produce the most homogeneous distribution in the groups or to tell if the two groups comes from the same distributions.

I am looking for a statistical measures mostly. Any suggestions?

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You can compute a similarity score between each couple of instances (diff in features) and then you can check if the distribution of the difference for each group (similar and dissimilar) is significantly different using the Kolmogorov-Smirnov test.

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    $\begingroup$ what do you do when the data is non continous? Per example binary or some categorical variables that you have encoded? $\endgroup$
    – Carlos Mougan
    Commented Jan 13, 2020 at 8:36
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    $\begingroup$ I guess if you have a non-ordinal categorical variables you can do one hot encoding of them and then apply the Chi-Square test instead. If the categorical variables are ordinal then do just min-max normalization between 0 to 1. $\endgroup$
    – HilaD
    Commented Jan 13, 2020 at 9:15

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