Low rank Euclidean distance matrix

How i can generate a random low rank EDM matrix X such that X=A*B and A of size (n,r), and B of size(r,n)

Answer 1

[Image Analyst]

I'm not sure what that means, but you can generate an EDM matrix with bwdist

[Hajar Alshaikh]

i mean like the following code , however this give me EDM matrix but i want this marix exactly to be a result of the multiplication of two matrices A in size n*r and B of size r*n

 Y = randn(n, r);

% Compute the Euclidean distance matrix (EDM) between points
X = zeros(n, n);
for i = 1:n
for j = i:n
dist = sqrt(sum((Y(i,:) - Y(j,:)).^2));
X(i,j) = dist;
X(j,i) = dist;
end
end

% Verify that X is a valid EDM
valid = true;
for i = 1:n
for j = i:n
if i == j && X(i,j) ~= 0
valid = false;
break;
elseif X(i,j) ~= X(j,i) || X(i,j) < 0
valid = false;
break;
end
end
end
if valid
disp('X is a valid EDM');
else
disp('X is not a valid EDM');
end

[Hajar Alshaikh]

You can notice here that X is EDM . However, it is not a low rank matrix . The rank of this X is n-1 which is not a low rank

[Image Analyst]

You're using EDM in a way that is not familiar to me, as a member of the image processing community, where it means the distance of a pixel in a foreground object to the nearest background pixel.

Your first loop looks like it's doing the same thing as pdist2

Sorry I can't help you because I don't understand why rank matters and why you want it to be a low number. Image image processing, the EDM is what it is - it's a given for a given matrix and is not something you can adjust. It's like saying the distance between 10 and 15 is 5. OK, it's 5 but you can't say that want it to be 4. It just isn't. So that's why I say I don't understand what you want or why you want it.