void mitk::ConnectomicsStatisticsCalculator::CalculateNormalizedLaplacianMetrics()
{
vnl_matrix<double> normalizedLaplacianMatrix(m_NumberOfVertices, m_NumberOfVertices, 0);
EdgeIteratorType ei, ei_end;
VertexDescriptorType sourceVertex, destinationVertex;
int sourceIndex, destinationIndex;
VertexIndexMapType vertexIndexMap = boost::get(boost::vertex_index, *(m_Network->GetBoostGraph()) );
m_VectorOfSortedNormalizedLaplacianEigenValues.clear();
// Normalized laplacian matrix
for( boost::tie(ei, ei_end) = boost::edges( *(m_Network->GetBoostGraph()) ); ei != ei_end; ++ei)
{
sourceVertex = boost::source(*ei, *(m_Network->GetBoostGraph()) );
sourceIndex = vertexIndexMap[sourceVertex];
destinationVertex = boost::target(*ei, *(m_Network->GetBoostGraph()) );
destinationIndex = vertexIndexMap[destinationVertex];
int sourceDegree = boost::out_degree(sourceVertex, *(m_Network->GetBoostGraph()) );
int destinationDegree = boost::out_degree(destinationVertex, *(m_Network->GetBoostGraph()) );
normalizedLaplacianMatrix.put(
sourceIndex, destinationIndex, -1 / (sqrt(double(sourceDegree * destinationDegree))));
normalizedLaplacianMatrix.put(
destinationIndex, sourceIndex, -1 / (sqrt(double(sourceDegree * destinationDegree))));
}
VertexIteratorType vi, vi_end;
for(boost::tie(vi, vi_end)=boost::vertices( *(m_Network->GetBoostGraph()) ); vi!=vi_end; ++vi)
{
if(boost::out_degree(*vi, *(m_Network->GetBoostGraph()) ) > 0)
{
normalizedLaplacianMatrix.put(vertexIndexMap[*vi], vertexIndexMap[*vi], 1);
}
}
//End of normalized laplacian matrix definition
vnl_symmetric_eigensystem <double>
normalizedLaplacianEigensystem(normalizedLaplacianMatrix);
double N1=0, C1=0, D1=0, E1=0, F1=0, b1=0;
double N2=0, C2=0, D2=0, E2=0, F2=0, b2=0;
m_NormalizedLaplacianNumberOf2s = 0;
m_NormalizedLaplacianNumberOf1s = 0;
m_NormalizedLaplacianNumberOf0s = 0;
m_NormalizedLaplacianTrace = 0;
m_NormalizedLaplacianEnergy = 0;
for(int i(0); i< m_NumberOfVertices; ++i)
{
double eigenValue = std::fabs(normalizedLaplacianEigensystem.get_eigenvalue(i));
m_VectorOfSortedNormalizedLaplacianEigenValues.push_back(eigenValue);
m_NormalizedLaplacianTrace += eigenValue;
m_NormalizedLaplacianEnergy += eigenValue * eigenValue;
//0
if(eigenValue < mitk::eps)
{
m_NormalizedLaplacianNumberOf0s++;
}
//Between 0 and 1.
else if(eigenValue > mitk::eps && eigenValue< 1 - mitk::eps)
{
C1 += i;
D1 += eigenValue;
E1 += i * eigenValue;
F1 += i * i;
N1 ++;
}
//1
else if(std::fabs( std::fabs(eigenValue) - 1) < mitk::eps)
{
m_NormalizedLaplacianNumberOf1s++;
}
//Between 1 and 2
else if(std::fabs(eigenValue) > 1+mitk::eps && std::fabs(eigenValue)< 2 - mitk::eps)
{
C2 += i;
D2 += eigenValue;
E2 += i * eigenValue;
F2 += i * i;
N2 ++;
}
//2
else if(std::fabs( std::fabs(eigenValue) - 2) < mitk::eps)
{
m_NormalizedLaplacianNumberOf2s++;
}
}
b1 = (D1*F1 - C1*E1)/(F1*N1 - C1*C1);
m_NormalizedLaplacianLowerSlope = (E1 - b1*C1)/F1;
b2 = (D2*F2 - C2*E2)/(F2*N2 - C2*C2);
m_NormalizedLaplacianUpperSlope = (E2 - b2*C2)/F2;
}
TEST(NormalizedLaplacianMatrixGTest, testSmallNormalizedLaplacianMatrix) {
NetworKit::Graph graph(7);
graph.addEdge(0, 1);
graph.addEdge(0, 4);
graph.addEdge(1, 4);
graph.addEdge(1, 2);
graph.addEdge(2, 3);
graph.addEdge(3, 4);
graph.addEdge(3, 5);
NormalizedLaplacianMatrix normalizedLaplacianMatrix(graph);
ASSERT_EQ(graph.numberOfNodes(), normalizedLaplacianMatrix.numberOfRows());
ASSERT_EQ(graph.numberOfNodes(), normalizedLaplacianMatrix.numberOfColumns());
EXPECT_EQ(1, normalizedLaplacianMatrix(0,0));
EXPECT_EQ(-1.0 / sqrt(2.0 * 3.0), normalizedLaplacianMatrix(0,1));
EXPECT_EQ(0, normalizedLaplacianMatrix(0,2));
EXPECT_EQ(0, normalizedLaplacianMatrix(0,3));
EXPECT_EQ(-1.0 / sqrt(2.0 * 3.0), normalizedLaplacianMatrix(0,4));
EXPECT_EQ(0, normalizedLaplacianMatrix(0,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(0,6));
EXPECT_EQ(1, normalizedLaplacianMatrix(1,1));
EXPECT_EQ(-1.0 / sqrt(2.0 * 3.0), normalizedLaplacianMatrix(1,2));
EXPECT_EQ(0, normalizedLaplacianMatrix(1,3));
EXPECT_EQ(-1.0 / 3.0, normalizedLaplacianMatrix(1,4));
EXPECT_EQ(0, normalizedLaplacianMatrix(1,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(1,6));
EXPECT_EQ(1, normalizedLaplacianMatrix(2,2));
EXPECT_EQ(-1.0 / sqrt(2.0 * 3.0), normalizedLaplacianMatrix(2,3));
EXPECT_EQ(0, normalizedLaplacianMatrix(2,4));
EXPECT_EQ(0, normalizedLaplacianMatrix(2,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(2,6));
EXPECT_EQ(1, normalizedLaplacianMatrix(3,3));
EXPECT_EQ(-1.0 / 3.0, normalizedLaplacianMatrix(3,4));
EXPECT_EQ(-1.0 / sqrt(3.0), normalizedLaplacianMatrix(3,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(3,6));
EXPECT_EQ(1, normalizedLaplacianMatrix(4,4));
EXPECT_EQ(0, normalizedLaplacianMatrix(4,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(4,6));
EXPECT_EQ(1, normalizedLaplacianMatrix(5,5));
EXPECT_EQ(0, normalizedLaplacianMatrix(5,6));
EXPECT_EQ(0, normalizedLaplacianMatrix(6,6));
}
