double GetAsstyCor(const PUNGraph& Graph) {
TIntFltH deg(Graph->GetNodes()), deg_sq(Graph->GetNodes());
for (TUNGraph::TNodeI NI = Graph->BegNI(); NI < Graph->EndNI(); NI++) {
deg.AddDat(NI.GetId()) = NI.GetOutDeg();
deg_sq.AddDat(NI.GetId()) = NI.GetOutDeg() * NI.GetOutDeg();
}
double m = Graph->GetEdges(), num1 = 0.0, num2 = 0.0, den1 = 0.0;
for (TUNGraph::TEdgeI EI = Graph->BegEI(); EI < Graph->EndEI(); EI++) {
double t1 = deg.GetDat(EI.GetSrcNId()).Val, t2 = deg.GetDat(EI.GetDstNId()).Val;
num1 += t1 * t2;
num2 += t1 + t2;
den1 += deg_sq.GetDat(EI.GetSrcNId()).Val + deg_sq.GetDat(EI.GetDstNId()).Val;
}
num1 /= m;
den1 /= (2.0 * m);
num2 = (num2 / (2.0 * m)) * (num2 / (2.0 * m));
return (num1 - num2) / (den1 - num2);
}
double BorgattiEverettMeasure(PUNGraph& Graph, TIntIntH& out, double coresize, int type) {
double sum = 0.0;
for (TUNGraph::TEdgeI EI = Graph->BegEI(); EI < Graph->EndEI(); EI++) { // Calculate and store the degrees of each node.
int i = EI.GetSrcNId();
int j = EI.GetDstNId();
if (type == 1) {
if (out.GetDat(i) == 1 || out.GetDat(j) == 1)
sum += 1;
}
else {
if (out.GetDat(i) == 1 && out.GetDat(j) == 1)
sum += 1;
}
}
return sum/(((coresize*coresize)-coresize)/2);
}
double PearsonCorrelation(PUNGraph& Graph, TIntIntH& out, int coresize) {
int br_core1=0,br_periphery1=0,br_core_per1=0;
for (TUNGraph::TEdgeI EI = Graph->BegEI(); EI < Graph->EndEI(); EI++) { // Calculate and store the degrees of each node.
int i = EI.GetSrcNId();
int j = EI.GetDstNId();
if (out.GetDat(i)==1&&out.GetDat(j)==1 && i!=j)
br_core1++;
else if (out.GetDat(i)==0&&out.GetDat(j)==0 && i!=j)
br_periphery1++;
else
br_core_per1++;
}
double core_quality = (double)br_core1/((((double)coresize*(double)coresize)-(double)coresize)/2);
int per_size = Graph->GetNodes()-coresize;
double periphery_quality = (((((double)per_size*(double)per_size)-(double)per_size)/2) - (double)br_periphery1)/((((double)per_size*(double)per_size)-(double)per_size)/2);
return (double)(core_quality+periphery_quality);
}
void GetMotifCount(const PUNGraph& G, const int MotifSize, TVec <int64> & MotifV, const int num) {
if (MotifSize == 3) {
MotifV = TVec <int64> (2);
MotifV.PutAll(0);
TSnap::GetTriads(G,MotifV[mtThreeClosed],MotifV[mtThreeOpen],num);
}
else {
MotifV = TVec <int64> (6);
MotifV.PutAll(0);
TIntPrV V(G->GetEdges(), 0);
for (TUNGraph::TEdgeI EI = G->BegEI(); EI < G->EndEI(); EI++) {
V.Add(TIntPr(EI.GetSrcNId(), EI.GetDstNId()));
}
TRnd blargh;
V.Shuffle(blargh);
for (int z = 0; z < num; z++) {
int SrcNId = V[z].Val1.Val, DstNId = V[z].Val2.Val;
TUNGraph::TNodeI SrcNI = G->GetNI(SrcNId), DstNI = G->GetNI(DstNId);
TIntV SrcV(SrcNI.GetOutDeg(),0), DstV(DstNI.GetOutDeg(),0), BothV(min(SrcNI.GetOutDeg(), DstNI.GetOutDeg()),0);
SrcV.Clr(0,-1);
DstV.Clr(0,-1);
BothV.Clr(0,-1);
//Grouping the vertices into sets
for (int e = 0; e < SrcNI.GetOutDeg(); e++) {
if (SrcNI.GetOutNId(e) == DstNId) continue;
if (G->IsEdge(DstNId, SrcNI.GetOutNId(e)) ) { BothV.Add(SrcNI.GetOutNId(e)); }
else { SrcV.Add(SrcNI.GetOutNId(e)); }
}
for (int e = 0; e < DstNI.GetOutDeg(); e++) {
if (DstNI.GetOutNId(e) == SrcNId) continue;
if (G->IsEdge(SrcNId, DstNI.GetOutNId(e)) == 0) { DstV.Add(DstNI.GetOutNId(e)); }
}
//Compute Motif 0 and 1
for (int i = 0; i < SrcV.Len(); i++) {
for (int j = 0; j < DstV.Len(); j++) {
if (G->IsEdge(SrcV[i], DstV[j]) ) { MotifV[mfFourSquare]++; }
else MotifV[mfFourLine]++;
}
}
//Compute Motif 2 and 3
for (int i = 0; i < SrcV.Len(); i++) {
for (int j = i + 1; j < SrcV.Len(); j++) {
if (G->IsEdge(SrcV[i], SrcV[j]) ) { MotifV[mfFourTriangleEdge]++; }
else MotifV[mfFourStar]++;
}
}
for (int i = 0; i < DstV.Len(); i++) {
for (int j = i + 1; j < DstV.Len(); j++) {
if (G->IsEdge(DstV[i], DstV[j]) ) { MotifV[mfFourTriangleEdge]++; }
else MotifV[mfFourStar]++;
}
}
//Compute Motif 4 and 5
for (int i = 0; i < BothV.Len(); i++) {
for (int j = i + 1; j < BothV.Len(); j++) {
if (G->IsEdge(BothV[i], BothV[j]) ) { MotifV[mfFourComplete]++; }
else MotifV[mfFourSquareDiag]++;
}
}
}
MotifV[mfFourSquare] /= 4ll;
MotifV[mfFourStar] /= 3ll;
MotifV[mfFourComplete] /= 6ll;
}
}
int TAGMFast::FindComsByCV(TIntV& ComsV, const double HOFrac, const int NumThreads, const TStr PlotLFNm, const double StepAlpha, const double StepBeta) {
if (ComsV.Len() == 0) {
int MaxComs = G->GetNodes() / 5;
ComsV.Add(2);
while(ComsV.Last() < MaxComs) { ComsV.Add(ComsV.Last() * 2); }
}
TIntPrV EdgeV(G->GetEdges(), 0);
for (TUNGraph::TEdgeI EI = G->BegEI(); EI < G->EndEI(); EI++) {
EdgeV.Add(TIntPr(EI.GetSrcNId(), EI.GetDstNId()));
}
EdgeV.Shuffle(Rnd);
int MaxIterCV = 3;
TVec<TVec<TIntSet> > HoldOutSets(MaxIterCV);
if (EdgeV.Len() > 50) { //if edges are many enough, use CV
printf("generating hold out set\n");
TIntV NIdV1, NIdV2;
G->GetNIdV(NIdV1);
G->GetNIdV(NIdV2);
for (int IterCV = 0; IterCV < MaxIterCV; IterCV++) {
// generate holdout sets
HoldOutSets[IterCV].Gen(G->GetNodes());
const int HOTotal = int(HOFrac * G->GetNodes() * (G->GetNodes() - 1) / 2.0);
int HOCnt = 0;
int HOEdges = (int) TMath::Round(HOFrac * G->GetEdges());
printf("holding out %d edges...\n", HOEdges);
for (int he = 0; he < (int) HOEdges; he++) {
HoldOutSets[IterCV][EdgeV[he].Val1].AddKey(EdgeV[he].Val2);
HoldOutSets[IterCV][EdgeV[he].Val2].AddKey(EdgeV[he].Val1);
HOCnt++;
}
printf("%d Edges hold out\n", HOCnt);
while(HOCnt++ < HOTotal) {
int SrcNID = Rnd.GetUniDevInt(G->GetNodes());
int DstNID = Rnd.GetUniDevInt(G->GetNodes());
HoldOutSets[IterCV][SrcNID].AddKey(DstNID);
HoldOutSets[IterCV][DstNID].AddKey(SrcNID);
}
}
printf("hold out set generated\n");
}
TFltV HOLV(ComsV.Len());
TIntFltPrV ComsLV;
for (int c = 0; c < ComsV.Len(); c++) {
const int Coms = ComsV[c];
printf("Try number of Coms:%d\n", Coms);
NeighborComInit(Coms);
printf("Initialized\n");
if (EdgeV.Len() > 50) { //if edges are many enough, use CV
for (int IterCV = 0; IterCV < MaxIterCV; IterCV++) {
HOVIDSV = HoldOutSets[IterCV];
if (NumThreads == 1) {
printf("MLE without parallelization begins\n");
MLEGradAscent(0.05, 10 * G->GetNodes(), "", StepAlpha, StepBeta);
} else {
printf("MLE with parallelization begins\n");
MLEGradAscentParallel(0.05, 100, NumThreads, "", StepAlpha, StepBeta);
}
double HOL = LikelihoodHoldOut();
HOL = HOL < 0? HOL: TFlt::Mn;
HOLV[c] += HOL;
}
}
else {
HOVIDSV.Gen(G->GetNodes());
MLEGradAscent(0.0001, 100 * G->GetNodes(), "");
double BIC = 2 * Likelihood() - (double) G->GetNodes() * Coms * 2.0 * log ( (double) G->GetNodes());
HOLV[c] = BIC;
}
}
int EstComs = 2;
double MaxL = TFlt::Mn;
printf("\n");
for (int c = 0; c < ComsV.Len(); c++) {
ComsLV.Add(TIntFltPr(ComsV[c].Val, HOLV[c].Val));
printf("%d(%f)\t", ComsV[c].Val, HOLV[c].Val);
if (MaxL < HOLV[c]) {
MaxL = HOLV[c];
EstComs = ComsV[c];
}
}
printf("\n");
RandomInit(EstComs);
HOVIDSV.Gen(G->GetNodes());
if (! PlotLFNm.Empty()) {
TGnuPlot::PlotValV(ComsLV, PlotLFNm, "hold-out likelihood", "communities", "likelihood");
}
return EstComs;
}