void PCA<T>::InitFromPointMatrix(DenseMatrix<T> &B)
{
const UINT PointCount = B.ColCount();
const UINT Dimension = B.RowCount();
Console::WriteLine(String("Initializing PCA, ") + String(B.ColCount()) + String(" points, ") + String(B.RowCount()) + String(" dimensions"));
_Means.Allocate(Dimension);
_Means.Clear(0.0);
for(UINT PointIndex = 0; PointIndex < PointCount; PointIndex++)
{
for(UINT DimensionIndex = 0; DimensionIndex < Dimension; DimensionIndex++)
{
_Means[DimensionIndex] += B.Cell(DimensionIndex, PointIndex);
}
}
for(UINT DimensionIndex = 0; DimensionIndex < Dimension; DimensionIndex++)
{
_Means[DimensionIndex] /= PointCount;
}
for(UINT PointIndex = 0; PointIndex < PointCount; PointIndex++)
{
for(UINT DimensionIndex = 0; DimensionIndex < Dimension; DimensionIndex++)
{
B.Cell(DimensionIndex, PointIndex) -= _Means[DimensionIndex];
}
}
DenseMatrix<T> C;
Console::WriteLine("Building correlation matrix...");
DenseMatrix<T>::MultiplyMMTranspose(C, B);
DenseMatrix<T>::MultiplyInPlace(C, T(1.0) / T(PointCount));
InitFromCorrelationMatrix(C);
}
void SpectralClustering::MakeLaplacian(const DenseMatrix<double> &S, Method method, DenseMatrix<double> &L)
{
const UINT pointCount = S.RowCount();
Vector<double> weightSums(pointCount, 0.0);
for(UINT outerPointIndex = 0; outerPointIndex < pointCount; outerPointIndex++)
{
for(UINT innerPointIndex = 0; innerPointIndex < pointCount; innerPointIndex++)
{
weightSums[outerPointIndex] += S(outerPointIndex, innerPointIndex);
}
}
if(method == Unnormalized || method == RandomWalk)
{
L = S;
for(UINT pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
L(pointIndex, pointIndex) = weightSums[pointIndex] - L(pointIndex, pointIndex);
}
if(method == RandomWalk)
{
for(UINT outerPointIndex = 0; outerPointIndex < pointCount; outerPointIndex++)
{
for(UINT innerPointIndex = 0; innerPointIndex < pointCount; innerPointIndex++)
{
L(outerPointIndex, innerPointIndex) /= weightSums[outerPointIndex];
}
}
}
}
if(method == Symmetric)
{
Vector<double> weightInvSqrts(pointCount);
for(UINT pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
weightInvSqrts[pointIndex] = sqrt(1.0f / weightSums[pointIndex]);
}
for(UINT outerPointIndex = 0; outerPointIndex < pointCount; outerPointIndex++)
{
for(UINT innerPointIndex = 0; innerPointIndex < pointCount; innerPointIndex++)
{
L(outerPointIndex, innerPointIndex) = S(outerPointIndex, innerPointIndex) * weightInvSqrts[outerPointIndex] * weightInvSqrts[innerPointIndex];
}
}
}
}
void PCA<T>::InitFromCorrelationMatrix(const DenseMatrix<T> &C)
{
const UINT Dimension = C.RowCount();
const bool OutputMatlabAndExit = false;
if(OutputMatlabAndExit)
{
Console::WriteLine("Outputting MATLAB matrix and exiting...");
C.SaveToMATLAB("C:\\MATLAB7\\work\\PCA.txt");
_Means.SaveToASCIIFile("C:\\JReaderData\\RawMeanVector.txt");
exit(0);
}
else
{
Console::WriteLine("Computing eigensystem...");
C.EigenSystem(_Eigenvalues, _Eigenvectors);
Console::WriteLine(C.EigenTest(_Eigenvalues, _Eigenvectors));
//_Eigenvectors.SaveToMATLAB("C:\\MATLAB7\\work\\MyEigenvectors.txt");
//_Eigenvalues.SaveToASCIIFile("C:\\MATLAB7\\work\\MyEigenvalues.txt");
}
FinalizeFromEigenSystem();
}
void SpectralClustering::Cluster(const DenseMatrix<double> &S, UINT kMeansClusters, UINT reducedDimensionCount, Method method, Vector<UINT> &clusterIDs, SpectralClusteringCache *cache)
{
const UINT pointCount = S.RowCount();
Console::WriteLine("Spectral clustering on " + String(pointCount) + " points, " + String(kMeansClusters) + " clusters, " + String(reducedDimensionCount) + String(" dimensions"));
DenseMatrix<double> L(pointCount, pointCount);
MakeLaplacian(S, method, L);
Vector<double> eigenvalues;
DenseMatrix<double> eigenvectors;
{
if(cache != NULL && cache->eigenvalues.Length() == pointCount)
{
Console::WriteString("Loading eigensystem from cache...");
eigenvalues = cache->eigenvalues;
eigenvectors = cache->eigenvectors;
}
else
{
Clock timer;
Console::WriteString("Solving eigensystem...");
L.EigenSystemTNT(eigenvalues, eigenvectors);
Console::WriteLine(String(timer.Elapsed()) + "s");
}
if(cache != NULL)
{
cache->eigenvalues = eigenvalues;
cache->eigenvectors = eigenvectors;
}
}
//
// Note that the eigensystem is sorted in decreasing order.
//
const bool useLargestEigenvector = (method == RandomWalk || method == Symmetric);
Vector<VecNf> points(pointCount);
for(UINT pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
VecNf &curPoint = points[pointIndex];
curPoint.v.Allocate(reducedDimensionCount);
for(UINT dimensionIndex = 0; dimensionIndex < reducedDimensionCount; dimensionIndex++)
{
if(useLargestEigenvector)
{
curPoint[dimensionIndex] = float(eigenvectors(pointIndex, pointCount - dimensionIndex - 1));
}
else
{
curPoint[dimensionIndex] = float(eigenvectors(pointIndex, dimensionIndex));
}
}
}
if(method == Symmetric)
{
for(UINT pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
points[pointIndex] = VecNf::Normalize(points[pointIndex]);
}
}
KMeansClustering<VecNf, VecNfKMeansMetric> clustering;
clustering.Cluster(points, kMeansClusters, 100);
clusterIDs.Allocate(pointCount);
for(UINT pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
clusterIDs[pointIndex] = clustering.QuantizeToNearestClusterIndex(points[pointIndex]);
}
}