Similarity datasets

Question

Given two (or maybe more) datasets with the same samples/members, but with different variables. Is there a general way to compare the information available in the two datasets without looking into the details of the variables?

So for example:

dataset1:

        | var1 | var2 | var3 | var4 | var5 | var6 |
sample1 |  7   |  4   |  5   |  3   |  3   |  4   |
sample2 |  9   |  4   |  5   |  4   |  8   |  2   |
sample3 |  7   |  5   |  1   |  9   |  4   |  3   |

dataset2:

        | var7 | var8 | var9 | var10| var11| var12|
sample1 |  3   |  7   |  1   |  2   |  8   |  7   |
sample2 |  6   |  3   |  3   |  6   |  8   |  4   |
sample3 |  3   |  1   |  4   |  3   |  2   |  6   |

How similar are these datasets?

Answer 1

So you want to know if any columns in the first data set exist disguised in the second one? How do you want to define similarity? You could start by standardizing both tables (subtract the column means and divide by the L^2 norm) then take the inner products of the matrices. The large elements in the resulting square, covariance matrix would correspond to the similar variables.