// to get first few eigenvectors
void GetEigVec(const PUNGraph& Graph, const int& EigVecs, TFltV& EigValV, TVec<TFltV>& EigVecV) {
const int Nodes = Graph->GetNodes();
// Lanczos
TUNGraphMtx GraphMtx(Graph);
int CalcVals = int(2*EigVecs);
if (CalcVals > Nodes) { CalcVals = Nodes; }
TFltVV EigVecVV;
//while (EigValV.Len() < EigVecs && CalcVals < 10*EigVecs) {
try {
TSparseSVD::Lanczos(GraphMtx, EigVecs, 2*EigVecs, ssotFull, EigValV, EigVecVV, false); }
catch(...) {
printf("\n ***EXCEPTION: TRIED %d GOT %d values** \n", CalcVals, EigValV.Len()); }
if (EigValV.Len() < EigVecs) {
printf(" ***TRIED %d GOT %d values** \n", CalcVals, EigValV.Len()); }
// CalcVals += EigVecs;
//}
TFltIntPrV EigValIdV;
for (int i = 0; i < EigValV.Len(); i++) {
EigValIdV.Add(TFltIntPr(EigValV[i], i));
}
EigValIdV.Sort(false);
EigValV.Sort(false);
for (int v = 0; v < EigValIdV.Len(); v++) { // vector components are not sorted!!!
EigVecV.Add();
EigVecVV.GetCol(EigValIdV[v].Val2, EigVecV.Last());
}
IsAllValVNeg(EigVecV[0], true);
}
void GetEigVals(const PUNGraph& Graph, const int& EigVals, TFltV& EigValV) {
// Lanczos
TUNGraphMtx GraphMtx(Graph);
//const int Nodes = Graph->GetNodes();
//int CalcVals = int(2*EigVals);
//if (CalcVals > Nodes) { CalcVals = Nodes; }
//while (EigValV.Len() < EigVals && CalcVals < 3*EigVals) {
try {
if (EigVals > 4) {
TSparseSVD::SimpleLanczos(GraphMtx, 2*EigVals, EigValV, false); }
else { TFltVV EigVecVV; // this is much more precise, but also much slower
TSparseSVD::Lanczos(GraphMtx, EigVals, 3*EigVals, ssotFull, EigValV, EigVecVV, false); }
}
catch(...) {
printf("\n ***EXCEPTION: TRIED %d GOT %d values** \n", 2*EigVals, EigValV.Len()); }
if (EigValV.Len() < EigVals) {
printf(" ***TRIED %d GOT %d values** \n", 2*EigVals, EigValV.Len()); }
// CalcVals += EigVals;
//}
EigValV.Sort(false);
/*if (EigValV.Len() > EigVals) {
EigValV.Del(EigVals, EigValV.Len()-1); }
else {
while (EigValV.Len() < EigVals) EigValV.Add(1e-6);
}
IAssert(EigValV.Len() == EigVals);*/
}
void PlotSngValRank(const PNGraph& Graph, const int& SngVals, const TStr& FNmPref, TStr DescStr) {
TFltV SngValV;
TSnap::GetSngVals(Graph, SngVals, SngValV);
SngValV.Sort(false);
if (DescStr.Empty()) { DescStr = FNmPref; }
TGnuPlot::PlotValV(SngValV, "sngVal."+FNmPref, TStr::Fmt("%s. G(%d, %d). Largest eig val = %f",
DescStr.CStr(), Graph->GetNodes(), Graph->GetEdges(), SngValV[0].Val), "Rank", "Singular value", gpsLog10XY, false, gpwLinesPoints);
}
void TNearestNeighbor::UpdateThreshold() {
ThresholdV.Gen(RateV.Len(), 0);
// sort distances
TFltV SortedV = DistV; SortedV.Sort(true);
// establish thrashold for each rate
for (const double Rate : RateV) {
// element Id corresponding to Rate-th percentile
const int Elt = (int)floor((1.0 - Rate) * SortedV.Len());
// remember the distance as threshold
ThresholdV.Add(SortedV[Elt]);
}
}
void TGraphKey::TakeSig(const PNGraph& Graph, const int& MnSvdGraph, const int& MxSvdGraph) {
const int Edges = Graph->GetEdges();
Nodes = Graph->GetNodes();
VariantId = 0;
SigV.Gen(2+Nodes, 0);
// degree sequence
TIntPrV DegV(Nodes, 0);
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
DegV.Add(TIntPr(NodeI.GetInDeg(), NodeI.GetOutDeg()));
}
DegV.Sort(false);
SigV.Add(TFlt(Nodes));
SigV.Add(TFlt(Edges));
for (int i = 0; i < DegV.Len(); i++) {
SigV.Add(DegV[i].Val1());
SigV.Add(DegV[i].Val2());
}
// singular values signature
// it turns out that it is cheaper to do brute force isomorphism
// checking than to calculate SVD and then check isomorphism
if (Nodes >= MnSvdGraph && Nodes < MxSvdGraph) {
// perform full SVD
TFltVV AdjMtx(Nodes+1, Nodes+1);
TFltV SngValV;
TFltVV LSingV, RSingV;
TIntH NodeIdH;
// create adjecency matrix
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
NodeIdH.AddKey(NodeI.GetId());
}
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
const int NodeId = NodeIdH.GetKeyId(NodeI.GetId()) + 1;
for (int e = 0; e < NodeI.GetOutDeg(); e++) {
const int DstNId = NodeIdH.GetKeyId(NodeI.GetOutNId(e)) + 1; // no self edges
if (NodeId != DstNId) AdjMtx.At(NodeId, DstNId) = 1;
}
}
try { // can fail to converge but results seem to be good
TSvd::Svd(AdjMtx, LSingV, SngValV, RSingV);
} catch(...) {
printf("\n***No SVD convergence: G(%d, %d): SngValV.Len():%d\n", Nodes(), Graph->GetEdges(), SngValV.Len());
}
// round singular values
SngValV.Sort(false);
for (int i = 0; i < SngValV.Len(); i++) {
SigV.Add(TMath::Round(SngValV[i], RoundTo));
}
}
//printf("SIG:\n"); for (int i = 0; i < SigV.Len(); i++) { printf("\t%f\n", SigV[i]); }
SigV.Pack();
}
void GetSngVals(const PNGraph& Graph, const int& SngVals, TFltV& SngValV) {
const int Nodes = Graph->GetNodes();
IAssert(SngVals > 0);
if (Nodes < 100) {
// perform full SVD
TFltVV AdjMtx(Nodes+1, Nodes+1);
TFltVV LSingV, RSingV;
TIntH NodeIdH;
// create adjecency matrix
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
NodeIdH.AddKey(NodeI.GetId()); }
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
const int NodeId = NodeIdH.GetKeyId(NodeI.GetId()) + 1;
for (int e = 0; e < NodeI.GetOutDeg(); e++) {
const int DstNId = NodeIdH.GetKeyId(NodeI.GetOutNId(e)) + 1; // no self edges
if (NodeId != DstNId) AdjMtx.At(NodeId, DstNId) = 1;
}
}
try { // can fail to converge but results seem to be good
TSvd::Svd1Based(AdjMtx, LSingV, SngValV, RSingV); }
catch(...) {
printf("\n***No SVD convergence: G(%d, %d)\n", Nodes, Graph->GetEdges()); }
} else {
// Lanczos
TNGraphMtx GraphMtx(Graph);
int CalcVals = int(2*SngVals);
//if (CalcVals > Nodes) { CalcVals = int(2*Nodes); }
//if (CalcVals > Nodes) { CalcVals = Nodes; }
//while (SngValV.Len() < SngVals && CalcVals < 10*SngVals) {
try {
if (SngVals > 4) {
TSparseSVD::SimpleLanczosSVD(GraphMtx, 2*SngVals, SngValV, false); }
else { TFltVV LSingV, RSingV; // this is much more precise, but also much slower
TSparseSVD::LanczosSVD(GraphMtx, SngVals, 3*SngVals, ssotFull, SngValV, LSingV, RSingV); }
}
catch(...) {
printf("\n ***EXCEPTION: TRIED %d GOT %d values** \n", 2*SngVals, SngValV.Len()); }
if (SngValV.Len() < SngVals) {
printf(" ***TRIED %d GOT %d values** \n", CalcVals, SngValV.Len()); }
// CalcVals += SngVals;
//}
}
SngValV.Sort(false);
//if (SngValV.Len() > SngVals) {
// SngValV.Del(SngVals, SngValV.Len()-1); }
//else {
// while (SngValV.Len() < SngVals) SngValV.Add(1e-6); }
//IAssert(SngValV.Len() == SngVals);
}
double TNetInfBs::GetBound(const TIntPr& Edge, double& CurProb) {
double Bound = 0;
TFltV Bounds;
// bound could be computed faster (using lazy evaluation, as in the optimization procedure)
for (int e=0; e < EdgeGainV.Len(); e++) {
const TIntPr& EE = EdgeGainV[e].Val2;
if (EE != Edge && !Graph->IsEdge(EE.Val1, EE.Val2)) {
const double EProb = GetAllCascProb(EE.Val1, EE.Val2);
if (EProb > CurProb) Bounds.Add(EProb - CurProb); }
}
Bounds.Sort(false);
for (int i=0; i<Graph->GetEdges() && i<Bounds.Len(); i++) Bound += Bounds[i];
return Bound;
}
void GetSngVec(const PNGraph& Graph, const int& SngVecs, TFltV& SngValV, TVec<TFltV>& LeftSV, TVec<TFltV>& RightSV) {
const int Nodes = Graph->GetNodes();
SngValV.Clr();
LeftSV.Clr();
RightSV.Clr();
TFltVV LSingV, RSingV;
if (Nodes < 100) {
// perform full SVD
TFltVV AdjMtx(Nodes+1, Nodes+1);
TIntH NodeIdH;
// create adjecency matrix (1-based)
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
NodeIdH.AddKey(NodeI.GetId()); }
for (TNGraph::TNodeI NodeI = Graph->BegNI(); NodeI < Graph->EndNI(); NodeI++) {
const int NodeId = NodeIdH.GetKeyId(NodeI.GetId())+1;
for (int e = 0; e < NodeI.GetOutDeg(); e++) {
const int DstNId = NodeIdH.GetKeyId(NodeI.GetOutNId(e))+1; // no self edges
if (NodeId != DstNId) AdjMtx.At(NodeId, DstNId) = 1;
}
}
try { // can fail to converge but results seem to be good
TSvd::Svd1Based(AdjMtx, LSingV, SngValV, RSingV);
} catch(...) {
printf("\n***No SVD convergence: G(%d, %d)\n", Nodes, Graph->GetEdges());
}
} else { // Lanczos
TNGraphMtx GraphMtx(Graph);
TSparseSVD::LanczosSVD(GraphMtx, SngVecs, 2*SngVecs, ssotFull, SngValV, LSingV, RSingV);
//TGAlg::SaveFullMtx(Graph, "adj_mtx.txt");
//TLAMisc::DumpTFltVVMjrSubMtrx(LSingV, LSingV.GetRows(), LSingV.GetCols(), "LSingV2.txt"); // save MTX
}
TFltIntPrV SngValIdV;
for (int i = 0; i < SngValV.Len(); i++) {
SngValIdV.Add(TFltIntPr(SngValV[i], i));
}
SngValIdV.Sort(false);
SngValV.Sort(false);
for (int v = 0; v < SngValIdV.Len(); v++) {
LeftSV.Add();
LSingV.GetCol(SngValIdV[v].Val2, LeftSV.Last());
RightSV.Add();
RSingV.GetCol(SngValIdV[v].Val2, RightSV.Last());
}
IsAllValVNeg(LeftSV[0], true);
IsAllValVNeg(RightSV[0], true);
}
// Computes GINI coefficient of egonet as a subset of the parent graph (edges into and out of the egonet ARE considered)
double TSnap::GetGiniCoefficient(const TIntFltH DegH, const TIntV NIdV) {
typename TIntV::TIter VI;
typename TFltV::TIter DI;
TFltV DegV;
const int n = NIdV.Len();
// DegV.Gen(n); // NOTE: don't use Gen() and Sort() on the same object (!)
for (VI = NIdV.BegI(); VI < NIdV.EndI(); VI++) {
DegV.Add(DegH.GetDat(VI->Val)); // might need to change this (in / out / undirected)
}
DegV.Sort();
int i = 0;
double numerator = 0.0, denominator = 0.0;
for (DI = DegV.BegI(); DI < DegV.EndI(); DI++, i++) {
numerator += (i + 1)*DegV[i];
denominator += DegV[i];
}
return(double(2*numerator) / double(n*denominator) - double(n + 1) / double(n));
}
void PlotSngValDistr(const PNGraph& Graph, const int& SngVals, const TStr& FNmPref, TStr DescStr) {
const int NBuckets = 50;
TFltV SngValV;
for (int f = 1; SngValV.Empty() && f < 4; f++) {
TSnap::GetSngVals(Graph, f*SngVals, SngValV);
}
SngValV.Sort(true);
THash<TFlt, TFlt> BucketCntH;
double Step = (SngValV.Last()-SngValV[0]) / double(NBuckets-1);
for (int i = 0; i < NBuckets; i++) {
BucketCntH.AddDat(SngValV[0]+Step*(i+0.5), 0);
}
for (int i = 0; i < SngValV.Len(); i++) {
const int Bucket = (int) floor((SngValV[i]-SngValV[0]) / Step);
BucketCntH[Bucket] += 1;
}
TFltPrV EigCntV;
BucketCntH.GetKeyDatPrV(EigCntV);
if (DescStr.Empty()) { DescStr = FNmPref; }
TGnuPlot::PlotValV(EigCntV, "sngDistr."+FNmPref, TStr::Fmt("%s. G(%d, %d). Largest eig val = %f", DescStr.CStr(),
Graph->GetNodes(), Graph->GetEdges(), SngValV.Last().Val), "Singular value", "Count", gpsAuto, false, gpwLinesPoints);
}
void TNetInfBs::GreedyOpt(const int& MxEdges) {
double CurProb = GetAllCascProb(-1, -1);
double LastGain = TFlt::Mx;
int attempts = 0;
bool msort = false;
for (int k = 0; k < MxEdges && EdgeGainV.Len() > 0; k++) {
double prev = CurProb;
const TIntPr BestE = GetBestEdge(CurProb, LastGain, msort, attempts);
if (BestE == TIntPr(-1, -1)) // if we cannot add more edges, we stop
break;
if (CompareGroundTruth) {
double precision = 0, recall = 0;
if (PrecisionRecall.Len() > 1) {
precision = PrecisionRecall[PrecisionRecall.Len()-1].Val2.Val;
recall = PrecisionRecall[PrecisionRecall.Len()-1].Val1.Val;
}
if (GroundTruth->IsEdge(BestE.Val1, BestE.Val2)) {
recall++;
} else {
precision++;
}
PrecisionRecall.Add(TPair<TFlt, TFlt>(recall, precision));
}
Graph->AddEdge(BestE.Val1, BestE.Val2); // add edge to network
double Bound = 0;
if (BoundOn)
Bound = GetBound(BestE, prev);
// localized update!
TIntV &CascsEdge = CascPerEdge.GetDat(BestE); // only check cascades that contain the edge
for (int c = 0; c < CascsEdge.Len(); c++) {
CascV[CascsEdge[c]].UpdateProb(BestE.Val1, BestE.Val2, true); // update probabilities
}
// some extra info for the added edge
TInt Vol; TFlt AverageTimeDiff; TFltV TimeDiffs;
Vol = 0; AverageTimeDiff = 0;
for (int i=0; i< CascV.Len(); i++) {
if (CascV[i].IsNode(BestE.Val2) && CascV[i].GetParent(BestE.Val2) == BestE.Val1) {
Vol += 1; TimeDiffs.Add(CascV[i].GetTm(BestE.Val2)-CascV[i].GetTm(BestE.Val1));
AverageTimeDiff += TimeDiffs[TimeDiffs.Len()-1]; }
}
AverageTimeDiff /= Vol;
if (TimeDiffs.Len() > 0)
TimeDiffs.Sort();
else
TimeDiffs.Add(0);
// compute bound only if explicitly required
EdgeInfoH.AddDat(BestE) = TEdgeInfo(Vol,
LastGain,
Bound,
TimeDiffs[(int)(TimeDiffs.Len()/2)],
AverageTimeDiff);
}
if (CompareGroundTruth) {
for (int i=0; i<PrecisionRecall.Len(); i++) {
PrecisionRecall[i].Val2 = 1.0 - PrecisionRecall[i].Val2/(PrecisionRecall[i].Val2+PrecisionRecall[i].Val1);
PrecisionRecall[i].Val1 /= (double)GroundTruth->GetEdges();
}
}
}
