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I have two matrices: A= 4000x78 where 78 is the dimension of features and 4000 is the number of samples. B= 1000x78 where 78 is the dimension of features and 1000 is the number of samples again.

Now, I want to see how the two samples are related based on their feature values. More specifically, I want to see how many samples in A are similar to each of the 1000 samples in B.

Apart from simple similarity (in terms of distance functions between each of the samples in A and B), can I use any other metrics (like correlation statistics) to understand the relationship between both?

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    $\begingroup$ Check their principal components. If they are from the same population they should be fairly similar. Also I think you are misleading potential readers with your title. You might attract a better crowd if you ask for 'similarity between two samples'. $\endgroup$ – usεr11852 says Reinstate Monic Mar 4 '15 at 9:25
  • $\begingroup$ I have reformatted the dimension of the matrices (in statistics we normally place the instance as rows and the measurements as columns) $\endgroup$ – user603 Mar 4 '15 at 12:14
  • $\begingroup$ You could aggregate the samples together and use a clustering algorithm. The makeup of the clusters will then tell you which of the samples in B are similar to those in A. $\endgroup$ – rwolst Mar 4 '15 at 12:20
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Have a look at the modified RV coefficient. This is a kind of correlation coefficient for matrices. See:

Smilde, A. K., Kiers, H. A. L., Bijlsma, S., Rubingh, C. M., & van Erk, M. J. (2009). Matrix correlations for high-dimensional data: the modified RV-coefficient. Bioinformatics, 25(3), 401–405.

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