Created
May 7, 2017 21:14
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Julia implementation of the motif-based clustering algorithm
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# Find a motif-based cluster for any directed triangle motif. | |
function MotifSpectralClust(A::SparseMatrixCSC{Int64,Int64}, motif::AbstractString) | |
# Form motif adjacency matrix | |
B = min.(A, A') # bidirectional links | |
U = A - B # unidirectional links | |
if motif == "M1" | |
C = (U * U) .* U' | |
W = C + C' | |
elseif motif == "M2" | |
C = (B * U) .* U' + (U * B) .* U' + (U * U) .* B | |
W = C + C' | |
elseif motif == "M3" | |
C = (B * B) .* U + (B * U) .* B + (U * B) .* B | |
W = C + C' | |
elseif motif == "M4" | |
W = (B * B) .* B | |
elseif motif == "M5" | |
C = (U * U) .* U + (U * U') .* U + (U' * U) .* U | |
W = C + C' | |
elseif motif == "M6" | |
W = (U * B) .* U + (B * U') .* U' + (U' * U) .* B | |
elseif motif == "M7" | |
W = (U' * B) .* U' + (B * U) .* U + (U * U') .* B | |
else | |
error("Motif must be one of M1, M2, M3, M4, M5, M6, or M7.") | |
end | |
# Get Fiedler eigenvector | |
dinvsqrt = spdiagm(1.0 ./ sqrt.(vec(sum(W, 1)))) | |
LM = I - dinvsqrt * W * dinvsqrt | |
lambdas, evecs = eigs(LM, nev=2, which=:SM) | |
z = dinvsqrt * real(evecs[:, 2]) | |
# Sweep cut | |
sigma = sortperm(z) | |
C = W[sigma, sigma] | |
Csums = sum(C, 1)' | |
motifvolS = cumsum(Csums) | |
motifvolSbar = sum(W) * ones(length(sigma)) - motifvolS | |
conductances = cumsum(Csums - 2 * sum(triu(C), 1)') ./ min.(motifvolS, motifvolSbar) | |
split = indmin(conductances) | |
if split <= length(size(A, 1) / 2) | |
return sigma[1:split] | |
else | |
return sigma[(split + 1):end] | |
end | |
end |
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