double TAGMUtil::GetConductance(const PUNGraph& Graph, const TIntSet& CmtyS, const int Edges) {
const int Edges2 = Edges >= 0 ? 2*Edges : Graph->GetEdges();
int Vol = 0, Cut = 0;
double Phi = 0.0;
for (int i = 0; i < CmtyS.Len(); i++) {
if (! Graph->IsNode(CmtyS[i])) {
continue;
}
TUNGraph::TNodeI NI = Graph->GetNI(CmtyS[i]);
for (int e = 0; e < NI.GetOutDeg(); e++) {
if (! CmtyS.IsKey(NI.GetOutNId(e))) {
Cut += 1;
}
}
Vol += NI.GetOutDeg();
}
// get conductance
if (Vol != Edges2) {
if (2 * Vol > Edges2) {
Phi = Cut / double (Edges2 - Vol);
}
else if (Vol == 0) {
Phi = 0.0;
}
else {
Phi = Cut / double(Vol);
}
} else {
if (Vol == Edges2) {
Phi = 1.0;
}
}
return Phi;
}
/// Newton method: DEPRECATED
int TAGMFast::MLENewton(const double& Thres, const int& MaxIter, const TStr PlotNm) {
TExeTm ExeTm;
int iter = 0, PrevIter = 0;
TIntFltPrV IterLV;
double PrevL = TFlt::Mn, CurL;
TUNGraph::TNodeI UI;
TIntV NIdxV;
G->GetNIdV(NIdxV);
int CID, UID, NewtonIter;
double Fuc, PrevFuc, Grad, H;
while(iter < MaxIter) {
NIdxV.Shuffle(Rnd);
for (int ui = 0; ui < F.Len(); ui++, iter++) {
if (! PlotNm.Empty() && iter % G->GetNodes() == 0) {
IterLV.Add(TIntFltPr(iter, Likelihood(false)));
}
UID = NIdxV[ui];
//find set of candidate c (we only need to consider c to which a neighbor of u belongs to)
TIntSet CIDSet;
UI = G->GetNI(UID);
if (UI.GetDeg() == 0) { //if the node is isolated, clear its membership and skip
if (! F[UID].Empty()) { F[UID].Clr(); }
continue;
}
for (int e = 0; e < UI.GetDeg(); e++) {
if (HOVIDSV[UID].IsKey(UI.GetNbrNId(e))) { continue; }
TIntFltH& NbhCIDH = F[UI.GetNbrNId(e)];
for (TIntFltH::TIter CI = NbhCIDH.BegI(); CI < NbhCIDH.EndI(); CI++) {
CIDSet.AddKey(CI.GetKey());
}
}
for (TIntFltH::TIter CI = F[UID].BegI(); CI < F[UID].EndI(); CI++) { //remove the community membership which U does not share with its neighbors
if (! CIDSet.IsKey(CI.GetKey())) {
DelCom(UID, CI.GetKey());
}
}
if (CIDSet.Empty()) { continue; }
for (TIntSet::TIter CI = CIDSet.BegI(); CI < CIDSet.EndI(); CI++) {
CID = CI.GetKey();
//optimize for UID, CID
//compute constants
TFltV AlphaKV(UI.GetDeg());
for (int e = 0; e < UI.GetDeg(); e++) {
if (HOVIDSV[UID].IsKey(UI.GetNbrNId(e))) { continue; }
AlphaKV[e] = (1 - PNoCom) * exp(- DotProduct(UID, UI.GetNbrNId(e)) + GetCom(UI.GetNbrNId(e), CID) * GetCom(UID, CID));
IAssertR(AlphaKV[e] <= 1.0, TStr::Fmt("AlphaKV=%f, %f, %f", AlphaKV[e].Val, PNoCom.Val, GetCom(UI.GetNbrNId(e), CID)));
}
Fuc = GetCom(UID, CID);
PrevFuc = Fuc;
Grad = GradientForOneVar(AlphaKV, UID, CID, Fuc), H = 0.0;
if (Grad <= 1e-3 && Grad >= -0.1) { continue; }
NewtonIter = 0;
while (NewtonIter++ < 10) {
Grad = GradientForOneVar(AlphaKV, UID, CID, Fuc), H = 0.0;
H = HessianForOneVar(AlphaKV, UID, CID, Fuc);
if (Fuc == 0.0 && Grad <= 0.0) { Grad = 0.0; }
if (fabs(Grad) < 1e-3) { break; }
if (H == 0.0) { Fuc = 0.0; break; }
double NewtonStep = - Grad / H;
if (NewtonStep < -0.5) { NewtonStep = - 0.5; }
Fuc += NewtonStep;
if (Fuc < 0.0) { Fuc = 0.0; }
}
if (Fuc == 0.0) {
DelCom(UID, CID);
}
else {
AddCom(UID, CID, Fuc);
}
}
}
if (iter - PrevIter >= 2 * G->GetNodes() && iter > 10000) {
PrevIter = iter;
CurL = Likelihood();
if (PrevL > TFlt::Mn && ! PlotNm.Empty()) {
printf("\r%d iterations, Likelihood: %f, Diff: %f", iter, CurL, CurL - PrevL);
}
fflush(stdout);
if (CurL - PrevL <= Thres * fabs(PrevL)) { break; }
else { PrevL = CurL; }
}
}
if (! PlotNm.Empty()) {
printf("\nMLE for Lambda completed with %d iterations(%s)\n", iter, ExeTm.GetTmStr());
TGnuPlot::PlotValV(IterLV, PlotNm + ".likelihood_Q");
}
return iter;
}