/
simple_glrms.jl
110 lines (100 loc) · 2.49 KB
/
simple_glrms.jl
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using LowRankModels
import StatsBase: sample
println("simple glrm examples")
# minimize ||A - XY||^2
function fit_pca(m,n,k)
# matrix to encode
A = randn(m,k)*randn(k,n)
loss = QuadLoss()
r = ZeroReg()
glrm = GLRM(A,loss,r,r,k)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
# minimize_{X>=0, Y>=0} ||A - XY||^2
function fit_nnmf(m,n,k)
# matrix to encode
A = rand(m,k)*rand(k,n)
loss = QuadLoss()
r = NonNegConstraint()
glrm = GLRM(A,loss,r,r,k)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
# minimize ||A - XY||^2 + .1||X||^2 + .1||Y||^2
function fit_pca_nucnorm(m,n,k)
# matrix to encode
A = randn(m,k)*randn(k,n)
loss = QuadLoss()
r = QuadReg(.1)
glrm = GLRM(A,loss,r,r,k)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
# minimize_{X<=0} ||A - XY||^2
function fit_kmeans(m,n,k)
# matrix to encode
Y = randn(k,n)
A = zeros(m,n)
for i=1:m
A[i,:] = Y[mod(i,k)+1,:]
end
loss = QuadLoss()
ry = ZeroReg()
rx = UnitOneSparseConstraint()
glrm = GLRM(A,loss,rx,ry,k+4)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
function fit_pca_nucnorm_sparse(m,n,k,s)
# matrix to encode
A = randn(m,k)*randn(k,n)
loss = QuadLoss()
r = QuadReg(.1)
obsx = sample(1:m,s); obsy = sample(1:n,s)
obs = [(obsx[i],obsy[i]) for i=1:s]
glrm = GLRM(A,loss,r,r,k, obs=obs)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
function fit_pca_nucnorm_sparse_nonuniform(m,n,k,s)
# matrix to encode
A = randn(m,k)*randn(k,n)
loss = QuadLoss()
r = QuadReg(.1)
obsx = [sample(1:round(Int,m/4),round(Int,s/2)); sample(round(Int,m/4)+1:m,s-round(Int,s/2))]
obsy = sample(1:n,s)
obs = [(obsx[i],obsy[i]) for i=1:s]
glrm = GLRM(A,loss,r,r,k, obs=obs)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
function fit_soft_kmeans(m,n,k)
# PCA with loadings constrained to lie on unit simplex
# constrain columns of X to lie on unit simplex
Xreal = rand(k,m)
Xreal ./= sum(Xreal,1)
A = Xreal' * randn(k,n)
loss = QuadLoss()
rx = SimplexConstraint()
ry = ZeroReg()
glrm = GLRM(A,loss,rx,ry,k)
X,Y,ch = fit!(glrm)
println("Convergence history:",ch.objective)
return A,X,Y,ch
end
if true
Random.seed!(10)
fit_pca(100,100,2)
fit_pca_nucnorm(100,100,2)
fit_pca_nucnorm_sparse(500,500,2,10000)
fit_pca_nucnorm_sparse_nonuniform(1000,1000,2,20000)
fit_kmeans(50,50,10)
fit_nnmf(50,50,2)
end