I have a matrix $A$ with $n$ rows and $2$ columns. I want to smooth (let's say moving average) each column resulting in a smoothed matrix $B$ with $p$ rows and $2$ columns with $p \lt n$.
I can smooth the columns by taking different permutations of the rows of $A$, maintaining the column structure. That is, for each permutation, I smooth both columns with that order. I want to show one of the permutations is the $\bf{closest}$ to the original matrix $A$.
I am not sure what is the closeness measure I should consider. Should I perform a canonical correlation between the permuted smoothed matrix $B$ and $A$?
Any insight will be appreciated. Thanks.