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Calculating Cosine Similarity in Julia for K-Means

I am making with an implementation of K-means clustering in Julia.

Figure out, and implement a modification of k-means that alternatively measure similarity by the angle between vectors.

So I assumed that one could use Cosine Similarity for this, I have made the code work with regular K-means by calculating th squared Euclidian Distance, by this:

Distances[:,i] = sum((X.-C[[i],:]).^2, dims=2) # Where C is center, Distances are added using the i-th center

I tried to do this by using cosine similarity such as this:

Distances[:, i] = sum(1 .- ((X*C[[i], :]).^2 /(sum(X.^2, dims=2).*(C[[i],:]'*C[[i],:]))))

But this seems to not be working.

Have I misunderstood the question or am I implementing it wrong?

Solution

  • In my Beta Machine Learning Package, module Utils, I implemented the distances as:

    using LinearAlgebra
"""L1 norm distance (aka _Manhattan Distance_)"""
l1_distance(x,y)     = sum(abs.(x-y))
"""Euclidean (L2) distance"""
l2_distance(x,y)     = norm(x-y)
"""Squared Euclidean (L2) distance"""
l2²_distance(x,y)    = norm(x-y)^2
"""Cosine distance"""
cosine_distance(x,y) = dot(x,y)/(norm(x)*norm(y))

    I then use them in the cluster module. Note that you need the standard library package LinearAlgebra.