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matlabhamming-distance

Matlab : How to implement a vectorized version for L1 distance calculation

I want to calculate the Hamming distance between vectors which are very high dimensional. A data point is a vector called as the feature. Assuming, each component f_i as an integer, it is represented in its binary form having say j bits. There are n = 900 feature components for each data point. The problem formulation is

Problem

The formula for Hamming distance between 2 different vectors is given in the picture below where j = number of bits

formula

For ex let n = 10 feature components,

f = [3,4,1,4,5,6,6,7,1,14];
g = [1,3,5,6,7,8,11,3,10,2];

Each component / element of the array is represented by its 16 bit binary representation using dec2bin(f_i,l)

I tried using dist = sum((f-g).^2,2)* 1/2^l where l= 16 bits but this does not make sense because there are 2 summations in the formula.

Solution

  • If I understand correctly, what you want is

    sum(bitxor(f,g))/2^l

    where l=16