Find distance between one point and a subset of other points.

I would like to find the distance between a point and all points in a matrix X, where : a subset of . Mathematically, this would correspond to a vector with entries equal to the elements of the following set:

,

One way to do this is the following:

[~,Dist_i] = knnsearch(X(i,:),X, 'K', n);
Dist_iJ = Dist_i(J);

However, this requires n nearest neighbor searches, so the above is not likely to scale well. Is there a fast, ideally built-in way to do this task?

Answer 1

[Image Analyst]

For example, with 2-D array X, and 4 points:

n = 4; % Whatever
X = rand(n, 2);
% Find distance between point 1 and all other points
allDistances = pdist2(X(1, :), X)
% Find distance between point 2 and all other points
allDistances = pdist2(X(2, :), X)
% Find distance between point 3 and all other points
allDistances = pdist2(X(3, :), X)
% And so on.

you get

allDistances =

0 0.137705462706709 0.300486552306604 0.770204210452277

allDistances =

0.137705462706709 0 0.176471014289295 0.648765114726253

allDistances =

0.300486552306604 0.176471014289295 0 0.596340359329654

Adapt as needed for other n.