How to measure the similarity between two vectors? [duplicate] - matlab

Question

This question already has an answer here:
How to measure the similarity of two data
(1 answer)
Closed 5 years ago.
I have two vectors for eg
Aideal=rand(256,1);
and
A_estimated=rand(256,1);
How can I measure the similarity ? By similarity I mean I want each element of A_estimated to be almost same as that of Aideal.
Can Anyone please help.

Answer 1

mae(A-B) % mean(abs(A-B)) % Average or mean value of array
sae(A-B) % sum(abs(A-B)) % Sum absolute error performance function
norm(A-B,1) % sum(abs(A-B)) % 1-norm of the vector, which is the sum of the element magnitudes.
norm(A-B,inf) % max(abs(A-B)) % maximum absolute row sum of the diff of vectors.
mse(A-B) % mean((A-B).^2) % Mean of Sum of squared error
sse(A-B) % sum((A-B).^2) % Sum of squared error
norm(A-B) % sqrt(sse(A-B))

Answer 2

If you want to compare two vectors with respecto cosine similarity below code is enough for you
function [similarity] = CosineSimilarity(x1,x2)
%--------------------------------------------------------------------------
% Syntax: [similarity] = CosineSimilarity(x1,x2);
%
% Definition: Cosine similarity is a measure of similarity between two
% non-zero vectors of an inner product space that measures
% the cosine of the angle between them. The cosine of 0° is
% 1, and it is less than 1 for any other angle. It is thus a
% judgment of orientation and not magnitude: two vectors
% with the same orientation have a cosine similarity of 1,
% two vectors at 90° have a similarity of 0, and two vectors
% diametrically opposed have a similarity of -1, independent
% of their magnitude. Cosine similarity is particularly used
% in positive space, where the outcome is neatly bounded in
% [0,1]. The name derives from the term "direction cosine":
% in this case, note that unit vectors are maximally
% "similar" if they're parallel and maximally "dissimilar"
% if they're orthogonal (perpendicular). This is analogous
% to the cosine, which is unity (maximum value) when the
% segments subtend a zero angle and zero (uncorrelated)
% when the segments are perpendicular.[1].
%
% Inputs: [x1] is a vector
% [x2] is a vector
%
% Outputs: [similarity] is between 0 and 1
%
% Complexity: No
%
% Dependencies No dependency.
%
% Author: Ugur Ayan, PhD
% ugur.ayan#ugurayan.com.tr
% http://www.ugurayan.com.tr
%
% Date: May 15, 2016
%
% Refrences [1] https://en.wikipedia.org/wiki/Cosine_similarity
%--------------------------------------------------------------------------
if ( length (x1) == length(x2) )
similarity = sum(x1.*x2) / (norm(x1) * norm(x2));
else
disp('Vectors dimensions does not match');
end