Eigenvector Clustering¶

Once the eigenvectors are obtained, we have a continuous solution for a discrete problem. In order to obtain an assigment for every pattern, it is needed to discretize the eigenvectors. Obtaining this discrete solution from eigenvectors often requires solving another clustering problem, albeit in a lower-dimensional space. That is, eigenvectors are treated as geometrical coordinates of a point set.

This library provides two methods two obtain the discrete solution:

Kmeans by means of Clustering.jl
The one proposed in Multiclass spectral clustering

using  Distances,SpectralClustering, Plots, Clustering
function circle(N::Integer , r1::Float64)
    x = []
    y = []    
    for j =1:N
        angle = rand(0.0:0.001:2*pi)
        v = r1*exp(im*angle)
        push!(x, real(v) + rand()*r1*0.2)
        push!(y, imag(v) + rand()*r1*0.2)        
    end    
    return hcat(x, y)
end
function circle_in_circle(N::Integer, r1::Float64, r2::Float64)
    circle_1 = circle(N, r1)
    circle_2 = circle(N, r2)
    
    return (vcat(circle_1, circle_2)', vcat(ones(N), ones(N)*2))
end


function weight(i::Integer, neigh, v, m)
    return exp.(-Distances.colwise(SqEuclidean(), m, v) / 7)
end
(data, labels) = circle_in_circle(500, 15.0, 5.0)
knnconfig = KNNNeighborhood(data, 15)
graph = create(knnconfig, weight, data)
pred_clustering_1 = clusterize(NgLaplacian(2), KMeansClusterizer(2), graph)
pred_clustering_2 = clusterize(NgLaplacian(2, false), YuEigenvectorRotation(), graph)
colors =[RGB(1.0, 0.0, 0.0), RGB(0, 1.0, 0.0)]
plt1 = scatter(data[1, :], data[2, :], 
               color=[colors[i] for i in pred_clustering_1.assignments],
               title="KMeans clustering")
plt2 = scatter(data[1, :], data[2, :], 
               color=[colors[i] for i in pred_clustering_2.assignments],
               title="YuEigenvectorRotation clustering")
Plots.plot(plt2, plt1, layout=(@layout Plots.grid(1,2)))

References¶

using DocUtils
display("text/html",bibliography(["stella2003multiclass"]))