How to measure the similarity of two data

Question

I am measuring the similarity of two data with same size is 20. That is

A=[0.915450999999999    0.908220499999997   0.900374999999996   0.890547499999996   0.88         


        

Answer 1

The best solution in MATLAB to calculate the distance between vectors is the pdist method:

http://www.mathworks.com/help/stats/pdist.html

It can use several metrics and it is quite well optimized. In the documantation these metrics are described very well.

pdist compares all rowvectors with all rowvectors in a matrix and returns all of these distances. For two vectors you have to put them in a matrix and you have to call pdist method using this matrix as input argument:

% A and B are the vectors of your example
X = [A; B];
D = pdist(X, 'cosine'); % D = 1.0875e-005

If you call pdist with a matrix with more lines the output will be a vector as well. For example:

% A and B are the vectors of your example
X = [A; A; B; B];
D = pdist(X, 'cosine');
% D = 1.0e-004 * [0    0.1087    0.1087    0.1087    0.1087    0.0000]

D(1) is A compared with A (1st row with 2nd row).

D(2) is A compared with B (1st row with 3rd row).

D(3) is A compared with B (1st row with 4th row).

D(4) is A compared with B (2nd row with 3rd row).

D(5) is A compared with B (2nd row with 4th row).

D(6) is B compared with B (3rd row with 4th row).

Few years ago we implemented a simulation environment where several vectors inherit from a virtual line-scan camera are compared, and we used this method. It works perfectly.

Answer 2

As suggested here, you could use cosine similarity, which finds the angle between two vectors. Similar vectors have a value close to 1 and dissimilar vectors have a value close to 0.

function d = cosSimilarity(u, v)
    d = dot(u,v)/(norm(u)*norm(v));
end