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utils.jl
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utils.jl
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using NetworkOP
using Random;
using LinearAlgebra;
using DataStructures;
using DelimitedFiles;
using Printf;
using Statistics;
using Clustering;
using SparseArrays;
using LightGraphs;
using LinearMaps;
using IterativeSolvers;
using Arpack;
using Optim;
using LaTeXStrings;
using Plots; pyplot()
#------------------------------------------------------------------------------------------------
# this function pick the edge by magnitude of edge flows,
# not appliable in practice, just serve as an upper bound
# on how well we can do
#------------------------------------------------------------------------------------------------
function ssl_flow(FN::FlowNetwork, flow_vec::Vector{Float64}, TrRatio=0.5; order="ascending", TrSet=Set{Int64}())
#--------------------------------------------------------------------------------------------
if (order == "ascending")
od = sortperm(abs.(flow_vec));
elseif (order == "descending")
od = sortperm(abs.(flow_vec), rev=true);
else
throw(ArgumentError("flowId: invalid option"));
end
#--------------------------------------------------------------------------------------------
for i in od
#----------------------------------------------------------------------------------------
push!(TrSet, i)
#----------------------------------------------------------------------------------------
if (length(TrSet) >= TrRatio * length(FN.EE))
break
end
#----------------------------------------------------------------------------------------
end
#--------------------------------------------------------------------------------------------
return TrSet, setdiff(Set(1:length(FN.EE)), TrSet);
end
#------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------
# select edge randomly
#------------------------------------------------------------------------------------------------
function ssl_rand(FN::FlowNetwork, TrRatio=0.5; TrSet=Set{Int64}())
#--------------------------------------------------------------------------------------------
od = randperm(MersenneTwister(0),length(FN.EE));
#--------------------------------------------------------------------------------------------
for i in od
#----------------------------------------------------------------------------------------
push!(TrSet, i)
#----------------------------------------------------------------------------------------
if (length(TrSet) >= TrRatio * length(FN.EE))
break
end
#----------------------------------------------------------------------------------------
end
#--------------------------------------------------------------------------------------------
@assert length(TrSet) == Int64(ceil(length(FN.EE)*TrRatio));
return TrSet, setdiff(Set(1:length(FN.EE)), TrSet);
end
#------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------
# select edge with RRQR algorithm
#------------------------------------------------------------------------------------------------
function al_rrqr(FN::FlowNetwork, TrRatio=0.5; TrSet=Set{Int64}())
TeId = collect(setdiff(Set(1:length(FN.EE)), TrSet));
od = qr(nullspace(Matrix(NetworkOP.mat_div(FN)))'[:,TeId],Val(true)).p;
union!(TrSet, TeId[od[1:Int64(ceil(length(FN.EE)*TrRatio))-length(TrSet)]]);
@assert length(TrSet) == Int64(ceil(length(FN.EE)*TrRatio));
return TrSet, setdiff(Set(1:length(FN.EE)), TrSet);
end
#------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------
# spectral embedding of vertices
#------------------------------------------------------------------------------------------------
function spectral_embedding(FN::FlowNetwork, ndim=2)
A = NetworkOP.mat_adj(FN); L = spdiagm(0=>vec(sum(A,dims=1)))-A;
tol = 1.0e-6+1.0; num_ev = ndim; result = nothing;
while (true)
global eigval,eigvec;
while true
try
eigval,eigvec = eigs(L+I, nev=num_ev+1, which=:SM, maxiter=3000);
break
catch
println("retry");
end
end
if (sum(eigval .> tol) >= ndim)
break
else
num_ev *= 2;
end
end
fid = findfirst(eigval .> tol);
X = collect(eigvec[:,fid:fid+1]');
return X;
end
#------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------
# select edge with RB algorithm
#------------------------------------------------------------------------------------------------
function al_rb(FN::FlowNetwork, TrRatio; ndim=2)
X = spectral_embedding(FN, ndim);
TrSet = Set{Int64}();
Clusters = OrderedDict{Int64,Vector{Int64}}(1=>collect(1:length(FN.VV)));
edge2id = Dict{Tuple{Int64,Int64},Int64}(idx=>i for (i,idx) in enumerate(keys(FN.EE)));
while (length(TrSet) < length(FN.EE) * TrRatio)
#-------------------------------------------------
# println(length(Clusters), " ", length(TrSet)/length(FN.EE))
#-------------------------------------------------
max_id = argmax([length(cluster) for cluster in values(Clusters)]);
cluster = Clusters[max_id];
Xc = X[:,cluster];
if (length(cluster) > 2)
if (all(isapprox.(Xc,Xc[:,1])))
cid = ones(Int64,length(cluster));
cid[Int64(ceil(0.5*length(cluster))):end] .= 2;
else
Random.seed!(0);
km = kmeans(Xc,2,init=:kmpp);
cid = assignments(km);
end
elseif (length(cluster) == 2)
cid = [1,2];
else
throw(ArgumentError("invalid cluster size"));
end
Clusters[max_id] = cluster[cid .== 1];
Clusters[length(Clusters)+1] = cluster[cid .== 2];
#-------------------------------------------------
for i in Clusters[max_id]
for j in Clusters[length(Clusters)]
idx = (min(i,j),max(i,j));
if (idx in keys(edge2id))
push!(TrSet, edge2id[idx]);
end
end
end
#-------------------------------------------------
end
cid = zeros(Int64,length(FN.VV));
for (i,cluster) in enumerate(values(Clusters))
cid[cluster] .= i;
end
return TrSet, setdiff(Set(1:length(FN.EE)), TrSet), X, cid;
end
#------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------
# this is the subroutine that actually performs the flow prediction
#------------------------------------------------------------------------------------------------
# FN: FlowNetwork object encoding the topology of the network (see modules/NetworkOP.jl)
# flow_vec: edge flows in a 1-d array, each element represents an edge
# ratio: desired ratio of the edges to be labelled
# flow_data: "ori" then the flow_vec is going to be used
# "syn" then create synthetic flows that is approximately divergence free
# algorithm: "zero_fill", alway predict zero flow for missing entries
# "line_graph", use vertex-based semi-supervised learning algorithm on the line-graph
# edge_set: "ascending", choose edges with the min edge flows
# "descending", choose edges with the max edge flows
# "random", choose edges by random
# "rrqr", choose edges with RRQR algorithm
# "rb", choose edges with RB algorithm
# lambda: regulation parameter, same lambda in the paper
#------------------------------------------------------------------------------------------------
# ratio: actual ratio of the edges to be labelled, this could differ from desired ratio due
# to either rounding, or when RB algorithm is used
# rate: correlation coefficient between ground truth and reconstructured edge flows
# flow_vec: edge flows in a 1-d array, useful when flow_data="syn"
# f_vec: reconstructured edge flows
# TrSet: labeled set of edges
# TeSet: unlabeled set of edges
#------------------------------------------------------------------------------------------------
function ssl_prediction(FN::FlowNetwork, flow_vec=nothing, ratio=0.5, flow_data="ori", algorithm="flow_regulation", edge_set="random", lambda=1.0e-1)
#--------------------------------------------------------------------------------------------
if (flow_data == "syn")
u,s,v = svd(Matrix{Float64}(NetworkOP.mat_div(FN)), full=true)
ss = vcat(s, zeros(length(FN.EE)-length(FN.VV)));
flow_vec = v * (1.0 ./ (ss .+ lambda))
else
@assert flow_vec != nothing;
end
#--------------------------------------------------------------------------------------------
#--------------------------------------------------------------------------------------------
if (edge_set in ["ascending", "descending"])
TrSet,TeSet = ssl_flow(FN, flow_vec, ratio; order=edge_set); TeId = collect(TeSet);
elseif (edge_set == "random")
TrSet,TeSet = ssl_rand(FN, ratio); TeId = collect(TeSet);
elseif (edge_set == "rrqr")
TrSet,TeSet = al_rrqr(FN, ratio); TeId = collect(TeSet);
elseif (edge_set == "rb")
TrSet,TeSet = al_rb(FN, ratio); TeId = collect(TeSet);
else
throw(ArgumentError());
end
ratio = length(TrSet)/length(FN.EE);
#--------------------------------------------------------------------------------------------
#--------------------------------------------------------------------------------------------
f0 = collect(flow_vec); f0[TeId] = zeros(length(TeId));
expand = ff->collect(sparsevec(TeId,ff,length(FN.EE)));
select = ff->ff[TeId];
#--------------------------------------------------------------------------------------------
if (algorithm == "flow_ssl")
indices = collect(keys(FN.EE));
lambda_vec = [lambda./sqrt(FN.VV[idx[1]] * FN.VV[idx[2]]) for idx in indices[TeId]];
op = LinearMap{Float64}(ff->vcat(NetworkOP.div(FN,expand(ff)), lambda_vec.*ff),
pp->select(NetworkOP.divT(FN,pp[1:length(FN.VV)])) + lambda_vec.*pp[length(FN.VV)+1:end],
length(FN.VV)+length(TeId), length(TeId); ismutating=false);
f, history = lsqr(op, vcat(-NetworkOP.div(FN,f0), lambda_vec.*zeros(length(TeId))); log=true, maxiter=1000);
f_vec = f0 + collect(expand(f));
elseif (algorithm == "line_graph")
LG = NetworkOP.line_graph(FN)
op = LinearMap{Float64}(pp->NetworkOP.divT(LG,expand(pp)),
ff->select(NetworkOP.div(LG,ff)),
length(LG.EE), length(TeId); ismutating=false);
f, history = lsqr(op, -NetworkOP.divT(LG,f0); log=true, maxiter=1000);
f_vec = f0 + expand(f);
elseif (algorithm == "zero_fill")
f_vec = collect(f0);
else
throw(ArgumentError());
end
#--------------------------------------------------------------------------------------------
rate = cor(flow_vec, f_vec);
err2 = norm(flow_vec - f_vec)/norm(flow_vec)
println(flow_data, " ", algorithm, " ", edge_set, " ", @sprintf("%.2f", ratio), " ", @sprintf("%+.2f", rate), " ", @sprintf("%+7.2f", err2));
return ratio, rate, flow_vec, f_vec, TrSet, TeSet;
end
#------------------------------------------------------------------------------------------------