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We have two matrices, $A$ and $B$, representing two different probability distributions, with dimensions, $m*n$ and $k*n$, respectively.

How can we calculate the Bhattacharya distance or another measure of similarity or dissimilarity between $A$ and $B$?

Here, $m$ and $k$ denote the number of variables captured by the two matrices $A$ and $B$. In general, $m$ and $k$ are not equal.

$n$ is the number of observations, which is the same across the two distributions.

Related Broader Question:

Combining Bhattacharya Distance (or A Measure of Similarity) --- across Different Variables (Properties)

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Using the Johnson-Lindenstrauss transformation, we can reduce the dimension of the larger dataset to be the same dimension as the smaller dataset and then compute the Bhattacharya distance.

Link: https://en.wikipedia.org/wiki/Johnson-Lindenstrauss_lemma

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    $\begingroup$ When the very same answer is acceptable for two questions, those questions must be duplicates! $\endgroup$
    – whuber
    Commented Jan 29, 2016 at 15:08
  • $\begingroup$ That makes this a part of the "bigger" question, then, doesn't it? The point is that the presence of the same answer, as well as the concept of a "bigger" question, indicate this entire thread is redundant. $\endgroup$
    – whuber
    Commented Jan 29, 2016 at 15:10
  • $\begingroup$ One thought would be to separate the original question into two separate threads, if you think that's possible. This thread would focus on its question and the other one would eliminate this question and focus on the second one--in which case you would want to delete the answer you posted there. $\endgroup$
    – whuber
    Commented Jan 29, 2016 at 16:54
  • $\begingroup$ @whuber Thanks for your suggestion. Please note, I have make them different questions now, but linked them together $\endgroup$
    – texmex
    Commented Feb 1, 2016 at 2:42

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