With R2018a, there is a new function matchpairs which might be useful for this. Basically, it takes a matrix of similarities between two sets, and matches these sets up in pairs.
Here's an example:
>> X = randn(100);
>> d = eig(X);
>> d2 = eig(X + randn(100)*1e-2);
>> max(abs(d - d2))
ans =
17.9169
>> m = matchpairs(abs(d - d2.'), 1e-1); % The columns of m map the elements of d to those of d2
>> max(abs(d(m(:, 1)) - d2(m(:, 2))))
ans =
0.1569
The second input to matchpairs gives a cutoff: If two values have a difference larger than 1e-1, they would not be matched at all, and would show up as a new eigenvalue and a disappeared eigenvalues instead.
