MATLAB short way to find closest vector?

Question

In my application, I need to find the "closest" (minimum Euclidean distance vector) to an input vector, among a set of vectors (i.e. a matrix)

Therefore every single time I have to do this :

function [match_col] = find_closest_column(input_vector, vectors)
cmin = 99999999999; % current minimum distance
match_col = -1;    

    for col=1:width
        candidate_vector = vectors(:,c); % structure of the input is not important
        dist = norm(input_vector - candidate_vector);
        if dist < cmin
            cmin = dist;
            match_col = col;
        end
    end

is there a built-in MATLAB function that does this kind of thing easily (with a short amount of code) for me ?

Thanks for any help !

Answer 1

Use pdist2. Assuming (from your code) that your vectors are columns, transposition is needed because pdist2 works with rows:

[cmin, match_col] = min(pdist2(vectors.', input_vector.' ,'euclidean'));

It can also be done with bsxfun (in this case it's easier to work directly with columns):

[cmin, match_col] = min(sum(bsxfun(@minus, vectors, input_vector).^2));
cmin = sqrt(cmin); %// to save operations, apply sqrt only to the minimizer 

Answer 2

norm can't be directly applied to every column or row of a matrix, so you can use arrayfun:

dist = arrayfun(@(col) norm(input_vector - candidate_vector(:,col)), 1:width);
[cmin, match_col] = min(dist);

This solution was also given here.

HOWEVER, this solution is much much slower than doing a direct computation using bsxfun (as in Luis Mendo's answer), so it should be avoided. arrayfun should be used for more complex functions, where a vectorized approach is harder to get at.