How to find minimal distance between elements?

Mr M. (view profile)

on 9 Mar 2018
Latest activity Commented on by Jan

on 15 Mar 2018

Roger Stafford (view profile)

I have a vector, and I would like to find the minimal distance between element values. Any element distance from any element in the set. Is it possible to do this without a for cycle?

Image Analyst

Image Analyst (view profile)

on 10 Mar 2018
Mr. M, you've now asked 311 questions and "Accepted" virtually none of them. Perhaps now you can "thank" the people who took their time to try to help you by Accepting their answers so that they get reputation points. That's the etiquette in this forum. Thanks in advance.

Roger Stafford (view profile)

on 9 Mar 2018
Edited by Roger Stafford

Roger Stafford (view profile)

on 9 Mar 2018

Let your vector be called v. Then do this:
d = min(diff(sort(v)));
This finds the minimum distance between any two elements of v, but it does not show the points in v where that occurs. To do that requires the use of the index returned as a second output of the 'sort' function as well as an index from the 'min' function. Let us know if that is what you want.

Guillaume

Guillaume (view profile)

on 9 Mar 2018
Indeed, as long as we're talking about a vector of numbers, this is the most efficient. To get the original indices of the two closest numbers:
v = randi(1000, 1, 10) %demo data
[sorted, originalidx] = sort(v);
[mindistance, where] = min(diff(sorted));
closestindex = originalidx([where, where+1]);
fprintf('elements at index %d and %d have got the minimum distance of %d\n', closestindex, mindistance)
Jan

Jan (view profile)

on 9 Mar 2018
+1. Sorting at first is the cheapest approach.

Von Duesenberg (view profile)

on 9 Mar 2018

This will get you started:
dumVect = [1 3 5 30]';
[minVal, idxMin] = min(diff(dumVect))
If you work with more dimensions, you may want to use pdist instead of diff. And of course, I'll let you figure out how you want to handle ties.

Jan

Jan (view profile)

on 9 Mar 2018
This is the minimal distance between neighboring elements, not between all elements.
Von Duesenberg

Von Duesenberg (view profile)

on 9 Mar 2018
Oops, you're right.

on 9 Mar 2018
Edited by Jan

Jan (view profile)

on 10 Mar 2018

n = 10;
v = rand(1, n);
dist = abs(v - v.'); % Auto-expand since R2016b
dist(1:(n+1):end) = Inf; % Mask the zeros [EDITED]
% dist = bsxfun(@minus, v, v.') .^ 2; % For older versions
[minValue, minIndex] = min(dist(:));

Show 1 older comment
Jan

Jan (view profile)

on 9 Mar 2018
@Jos: Of course 0 is the correct answer to the original question: "Any element distance from any element in the set". This includes the distance from an element to itself, which is zero. :-)
Of course, this was not meant, and I have edited the code now to solve: "Any element distance from any other element in the set".
Thanks for finding my mistake.
Mr M.

Mr M. (view profile)

on 14 Mar 2018
What is this? v.'
Jan

Jan (view profile)

on 15 Mar 2018
@Mr M.: You can simply try it.
v = rand(2,3)
v.'
It is the transpose operator. The quote without the dot before replies the conjugate complex value in addition.

Image Analyst (view profile)

on 9 Mar 2018

If the "vector" is actually a matrix of (x,y) locations, you can use pdist2(). Let me know if that's the case and I'll give you an example.

Jos (10584) (view profile)

on 9 Mar 2018
Edited by Jos (10584)

Jos (10584) (view profile)

on 9 Mar 2018

By definition the minimum distance is zero because v(i)==v(i) for any element i of the vector v.
But I assume you want the minimum distance between v(i) and v(j) for all pairs (i,j) where i is unequal to j, but forgot to mention that ... :p

Mr M.

on 14 Mar 2018
yes, of course

Jos (10584) (view profile)

on 9 Mar 2018

Without creating a possibly large intermediate N-ny-N matrix or using a possibly slow sort
V = [1 8 6 4 2 10] ;
W = nchoose2(V) % all pairs of distinct elements
D = abs(W(:,2)-W(:,1)) % distance between pairs
[minD, ix] = min(D) % minD = 1
minPair = W(ix,:) % minPair = [1 2]
nchoose2 is a fast function to get all combinations of two elements, and can be downloaded from the Matlab File Exchange: https://uk.mathworks.com/matlabcentral/fileexchange/20144-nchoose2-x-