How to find k nearest vectors from a given vector in 3 dimensions ?

I have a reference vector and I want to find a fixed k nearest neighbors from a matrix ? How can I do it? Is there any direct way?

[Walter Roberson]

When you say "reference vector", do you mean a line defined in N-dimensional space? And you want to find the k points that lie nearest to the line using Euclidean distance? Or does "reference vector" just mean an N-dimensional point and you want to find its k nearest neighbours using a distance measure you have not specified, possibly Euclidean distance?

Answer 1

[Star Strider]

This is one way:

V = randi(50,  1, 3);                   % Vector
M = randi(50, 15, 3);                   % Matrix
% 
dif = bsxfun(@minus, V, M);             % Subtract Vector from Matrix
D = sqrt(sum(dif.^2,2));                % Euclidean Distance Metric
[Ds,Ix] = sort(D,'ascend');             % Sort Ascending
k = 5;                                  % Number Of Neighbours
KNN = M(Ix(1:k),:);                     % K-th Nearest Neighbours

This simply finds them. If you have the Statistics Toolbox, the pdist2 function is likely more efficient.

Answer 2

[Walter Roberson]

If "reference vector" is a line then according to Roger Stafford over here

Let Q1 and Q2 be any two distinct points of the line and P the point in question, then

   d = norm(cross(Q2-Q1,P-Q1))/norm(Q2-Q1);

will give the requested orthogonal distance.