Averaged Euclidean Distance

1

Suppose we have a matrix A composed of m vectors with n dimensions.

And suppose we want to get the averaged Euclidean distance between all of those vectors. I know how to do this in for loops but I am not quite as clear for matrix operations.

I see someone posed the question here and received an answer:

Average distance in distance matrix - Cross Validated

How would this be implemented in Pytorch as a matrix operation?

Additionally, how would it need to be modified if the matrix is complex(i.e. torch.cfloat)?

2

So I found torch.cdist creates a Euclidean distance matrix.

So getting the average shouldn’t be an issue.

I noticed cdist doesn’t support complex matrices. But that’s fine. I can just do this:

vector_dims=10
n_vectors=100

A = torch.rand(n_vectors, vector_dims, dtype=torch.cfloat)

B = torch.cdist(A.real, A.real)

C = torch.cdist(A.imag, A.imag)

E_dist = (B**2 + C**2)**0.5

Avg_dist = torch.sum(E_dist) / (n_vectors*(n_vectors-1)))