包含字符串的成对距离矩阵

Question

I need to calculate the pairwise distance between two matrix elements in a way that distance is equal to the number of binary differences between features/dimensions. I want to do this with MATLAB codes without using a loop. For example: Assume I want to calculate the distance between instances in A and B :

A = [ 1 2 3 ; 2 3 4]         % (two instances with three features)

B = [ 2 3 4 ; 2 5 6 ; 4 5 6] % (three instances with three features)

I need to calculate C , which would be a 2x3 matrix contain the distance of instances in A and B in a way that the distance between [1 3 3] and [2 3 4] would be 2: comparing the features, when a feature is equivalent, add 0 to distance and when they are dissimilar add 1 to distance. So in this case,

C = [3 3 3; 0 2 3].

A and B may contain strings instead of numbers.

Answer 1

You can use bsxfun with @ne (not equal), followed by a sum to count the number of dissimilar features for an instance:

A = [1 2 3; 2 3 4];
B = [2 3 4; 2 5 6; 4 5 6];
C = squeeze(sum(bsxfun(@ne,A,permute(B,[3 2 1])),2))

C =

     3     3     3
     0     2     3

The above works by generating a logical array testing for equality of each feature for each instance pair via bsxfun(@ne,...) . Then a sum is performed over dimension 2 to count the number of dissimilar features for each instance.

Answer 2

The function pdist2 with Hamming distance already does this for you:

pdist2(A,B,'hamming')

This gives the result as percentage of coordinates that differ. Since you want number instead of percentage, multiply by the number of columns:

pdist2(A,B,'hamming')*size(A,2)

ans =

     3     3     3
     0     2     3