private void determineBiPartitionOfGraph(Vector<double> secondLargestEigVec, SpectralTreeNode spectralTreeRoot,
out List<int> firstPartIdx, out List<int> secondPartIdx)
{
firstPartIdx = new List<int>();
secondPartIdx = new List<int>();
List<int> firstPart = new List<int>();
List<int> secondPart = new List<int>();
for (int idx = 0; idx < secondLargestEigVec.Count; idx++)
{
if (secondLargestEigVec[idx] >= 0)
{
firstPartIdx.Add(idx);
firstPart.Add(spectralTreeRoot.VertexList[idx]);
}
else
{
secondPartIdx.Add(idx);
secondPart.Add(spectralTreeRoot.VertexList[idx]);
}
}
SpectralTreeNode spectralFirstTreeNode = new SpectralTreeNode() { VertexList = firstPart };
spectralTreeRoot.FirstChild = spectralFirstTreeNode;
SpectralTreeNode spectralSecondTreeNode = new SpectralTreeNode() { VertexList = secondPart };
spectralTreeRoot.SecondChild = spectralSecondTreeNode;
}
public double computeMeasure(SpectralTreeNode[] spectralTreeLeaves)
{
double measure = 0.0;
foreach (var spectralTreeLeaf in spectralTreeLeaves)
{
measure += computeMeasureForRegion(spectralTreeLeaf);
}
measure = measure / (double)serverNO;
return measure;
}
public SpectralTreeNode[] apply(int vertexNO)
{
SpectralTreeNode spectralTreeRoot = new SpectralTreeNode()
{
VertexList = Enumerable.Range(0, vertexNO).ToList()
};
innerDetermineNormCutAndChildren(spectralTreeRoot, weightMX);
innerDeterminePartition(spectralTreeRoot.FirstChild, spectralTreeRoot.SecondChild);
return listOfLeaves.ToArray();
}
public double computeMeasureForRegion(SpectralTreeNode spectralTreeLeaf)
{
double measureForRegion = 0.0;
int binNOInRegionWithoutZeroHeft = 0;
foreach (var vertexIdx in spectralTreeLeaf.VertexList)
{
int[] indicesArrayOfBin = new int[spaceDimension];
transformator.transformCellIdxToIndicesArray(histogramResolution, indicesArrayOfBin, vertexIdx);
int binValue = (int)histogram.GetValue(indicesArrayOfBin);
if (binValue > 0)
{
binNOInRegionWithoutZeroHeft++;
measureForRegion += computeMeasureForBin(indicesArrayOfBin, spectralTreeLeaf);
}
}
measureForRegion = measureForRegion / (double)binNOInRegionWithoutZeroHeft;
return measureForRegion;
}
public double computeMeasureForBin(int[] indicesArrayOfBin, SpectralTreeNode spectralTreeLeaf)
{
double measureForBin = 0.0;
int binValue = (int)histogram.GetValue(indicesArrayOfBin);
int currentKNN = (kNN < pointNO) ? kNN : pointNO - 1;
int nnInServer = binValue - 1;
int nnOutserver = 0;
if (currentKNN - binValue + 1 > 0)
{
Shell[] currentShells = new Shell[currentKNN - binValue + 1];
Array.Copy(shells, currentShells, currentKNN - binValue + 1);
var dictOfShells = transformator.convertIntPairsOfShellsToListOfIdxArrays(
histogramResolution, indicesArrayOfBin, shells);
iterateOverShells(spectralTreeLeaf, currentKNN, ref nnInServer, ref nnOutserver, dictOfShells);
}
//nnInServer should not be greater than (kNN - nnOutserver) because nnOutserver has been 'commited':
nnInServer = (nnInServer <= currentKNN - nnOutserver) ? nnInServer : currentKNN - nnOutserver;
measureForBin = (double)nnInServer / (double)currentKNN;
return measureForBin;
}
private bool isIdxArrayInTheSpectralTreeLeaf(int[] idxArray, SpectralTreeNode spectralTreeLeaf)
{
bool result = false;
int targetVertexIdx = transformator.transformIndicesArrayToCellIdx(histogramResolution, idxArray);
foreach (var vertexIdx in spectralTreeLeaf.VertexList)
{
if (targetVertexIdx == vertexIdx)
{
result = true;
}
}
return result;
}
private void updateNNCountsWithBinsOnCurrentShell(SpectralTreeNode spectralTreeLeaf, ref int nnInServer,
ref int tmpNNOutServer, List<int[]> idxArraysOnCurrentShell)
{
foreach (var idxArray in idxArraysOnCurrentShell)
{
int currentBinValue = (int)histogram.GetValue(idxArray);
if (isIdxArrayInTheSpectralTreeLeaf(idxArray, spectralTreeLeaf))
{
nnInServer += currentBinValue;
}
else
{
tmpNNOutServer += currentBinValue;
}
}
}
private void iterateOverShells(SpectralTreeNode spectralTreeLeaf, int kNN, ref int nnInServer, ref int nnOutserver,
Dictionary<int, List<int[]>> dictOfShells)
{
foreach (var shellIdx in dictOfShells.Keys)
{
int tmpNNOutServer = 0;
List<int[]> idxArraysOnCurrentShell = dictOfShells[shellIdx];
updateNNCountsWithBinsOnCurrentShell(spectralTreeLeaf, ref nnInServer, ref tmpNNOutServer,
idxArraysOnCurrentShell);
if (nnInServer + nnOutserver >= kNN)
{
break;
}
else
{
if (nnInServer + nnOutserver + tmpNNOutServer >= kNN)
{
nnOutserver = kNN - nnInServer;
break;
}
else
{
nnOutserver += tmpNNOutServer;
}
}
}
}
private void innerDeterminePartition(SpectralTreeNode spectralTreeNode1, SpectralTreeNode spectralTreeNode2)
{
innerDetermineNormCutAndChildren(spectralTreeNode1, determinePartOfWeightMX(spectralTreeNode1.VertexList));
innerDetermineNormCutAndChildren(spectralTreeNode2, determinePartOfWeightMX(spectralTreeNode2.VertexList));
listOfLeaves.Add(spectralTreeNode1);
listOfLeaves.Add(spectralTreeNode2);
if (listOfLeaves.Count < serverNO)
{
listOfLeaves.Sort(comparer);
SpectralTreeNode leafWithMinNormCut = listOfLeaves[0];
SpectralTreeNode firstChildOfLeafWithMinNormCut = leafWithMinNormCut.FirstChild;
SpectralTreeNode secondChildOfLeafWithMinNormCut = leafWithMinNormCut.SecondChild;
listOfLeaves.Remove(leafWithMinNormCut);
innerDeterminePartition(firstChildOfLeafWithMinNormCut, secondChildOfLeafWithMinNormCut);
}
}
private void innerDetermineNormCutAndChildren(SpectralTreeNode spectralTreeRoot, Matrix<double> partOfWeightMX)
{
Matrix<double> randomWalkMX = randomWalkDesigner.createPageRankMX(partOfWeightMX, alpha);
Vector<double> pi = randomWalkDesigner.createStationaryDistributionOf(randomWalkMX);
Matrix<double> theta = thetaMatrixFormation.createThetaMX(randomWalkMX, pi);
Vector<double> secondLargestEigVec = thetaMatrixFormation.determineSecondLargestEigVec(theta);
List<int> firstPartIdx, secondPartIdx;
determineBiPartitionOfGraph(secondLargestEigVec, spectralTreeRoot, out firstPartIdx, out secondPartIdx);
double normCutValue = determineNormCut(randomWalkMX, pi, firstPartIdx, secondPartIdx);
spectralTreeRoot.NormCutValue = normCutValue;
}
