Newbie: Euclidean distance of a matrix??

hello all, i am new to use matlab so guys i need ur help in this regards. if i have a mxn matrix e.g

X=[5 3 1; 2 5 6; 1 3 2]
i would like to compute the distance matrix for this given matrix as
D= [d11 d12 d13; d21 d22 d23; d31 d32 d33]

where d(ij)= euclidean distance between row i and j.

in my thinking i applied a for loop like this

% for r=1:rows
%     for c=1:cols
%         for k=1:3
%     d(r,c)= sqrt(sum(a(r,k)-a(c,k)).^2);
%         end
%     end
% end

but this thing doen't gives the desired result. can some one please correct me and also it would b nice if it would be not only for 3x3 matrix but for any mxn matrix..

thanks alot in advance i wish a nice smilling day

Answer 1

[Sean de Wolski]

Following your rules:

X=[5 3 1; 2 5 6; 1 3 2]; %sample matrix
myEdist = squeeze(sqrt(sum(bsxfun(@minus,X,reshape(X',1,size(X,2),size(X,1))).^2,2))) %Engine

Take the difference of elements in each combination of rows. Square it, sum it, root it, and squeeze it!.

[Usman Ali]

that works absolutly perfect. but i have another matrix of size 10x6, applied your code and found that the ans came out to be squared root of the original Ans to be expected.

so i changed a little bit of ur code by removing sqrt(). or by squaring myEdist and then the ans was perfectly matching.

i.e

myEdist = squeeze(sum(bsxfun(@minus,X,reshape(X',1,size(X,2),size(X,1))).^2,2))

or

myEdist = squeeze(sqrt(sum(bsxfun(@minus,X,reshape(X',1,size(X,2),size(X,1))).^2,2))).^2

but when i applied the new edited code back to old 3x3 matrix. the ans was the squared of the expected ans. so i have to take again the sqrt(ans).

would it b possible to think not only for the square matrices but of any size MxN

Answer 2

[Thomas]

Dunno if this is what you need:

X=[5 3 1; 2 5 6; 1 3 2]
for i=1:length(X)
dist(i,:)=pdist(X(:,i),'euclidean')';
end
dist

EDIT

All you need is

X=[5 3 1; 2 5 6; 1 3 2]
pdist(X)

or if you need a 3x3 matrix of output:

for i=1:length(X)
Y=circshift(X,i+1);
q(i,:)=pdist(Y);
q(i,i)=0;
end
q

Using Teja's comment might be the easiest:

X=[5 3 1; 2 5 6; 1 3 2]
squareform(pdist(X));

[Usman Ali]

unfortunatlly thats also incorrect.

actually any distance e.g d12 could be found as

1st row minus 2nd row, square each value, add all the values in a row vector and then take the sqrt i.e

1. sum =(x(1,1)-x(2,1)).^2 + (x(1,2)-x(2,2)).^2 + (x(1,3)-x(2,3)).^2

2. d12= sqrt(sum)

so in above example the ans should be d12=d21= 6.1644

[Teja Muppirala]

X=[5 3 1; 2 5 6; 1 3 2]

squareform(pdist(X))

will convert it into the 3x3 matrix