void mitk::ConnectomicsSimulatedAnnealingPermutationModularity::removeModule(
ToModuleMapType *vertexToModuleMap, int module )
{
int lastModuleNumber = getNumberOfModules( vertexToModuleMap ) - 1;
if( module == lastModuleNumber )
{
// no need to do anything, the last module is deleted "automatically"
return;
}
if( getNumberOfVerticesInModule( vertexToModuleMap, module ) > 0 )
{
MBI_WARN << "Trying to remove non-empty module";
return;
}
ToModuleMapType::iterator iter = vertexToModuleMap->begin();
ToModuleMapType::iterator end = vertexToModuleMap->end();
while( iter != end )
{
if( iter->second == lastModuleNumber )
{
// renumber last module to to-be-deleted module
iter->second = module;
}
iter++;
}
}
void mitk::ConnectomicsSimulatedAnnealingPermutationModularity::CleanUp()
{
// delete empty modules, if any
for( int loop( 0 ); loop < getNumberOfModules( &m_BestSolution ) ; loop++ )
{
if( getNumberOfVerticesInModule( &m_BestSolution, loop ) < 1 )
{
removeModule( &m_BestSolution, loop );
}
}
}
void mitk::ConnectomicsSimulatedAnnealingPermutationModularity::permutateMappingModuleChange(
ToModuleMapType *vertexToModuleMap, double currentTemperature, mitk::ConnectomicsNetwork::Pointer network )
{
//the random number generators
vnl_random rng( (unsigned int) rand() );
//randomly generate threshold
const double threshold = rng.drand64( 0.0 , 1.0);
//for deciding whether to join two modules or split one
double splitThreshold = 0.5;
//stores whether to join or two split
bool joinModules( false );
//select random module
int numberOfModules = getNumberOfModules( vertexToModuleMap );
unsigned long randomModuleA = rng.lrand32( numberOfModules - 1 );
//select the second module to join, if joining
unsigned long randomModuleB = rng.lrand32( numberOfModules - 1 );
if( ( threshold < splitThreshold ) && ( randomModuleA != randomModuleB ) )
{
joinModules = true;
}
if( joinModules )
{
// this being an kommutative operation, we will always join B to A
joinTwoModules( vertexToModuleMap, randomModuleA, randomModuleB );
//eliminate the empty module
removeModule( vertexToModuleMap, randomModuleB );
}
else
{
//split module
splitModule( vertexToModuleMap, currentTemperature, network, randomModuleA );
}
}
void mitk::ConnectomicsSimulatedAnnealingPermutationModularity::permutateMappingSingleNodeShift(
ToModuleMapType *vertexToModuleMap, mitk::ConnectomicsNetwork::Pointer network )
{
const int nodeCount = vertexToModuleMap->size();
const int moduleCount = getNumberOfModules( vertexToModuleMap );
// the random number generators
vnl_random rng( (unsigned int) rand() );
unsigned long randomNode = rng.lrand32( nodeCount - 1 );
// move the node either to any existing module, or to its own
//unsigned long randomModule = rng.lrand32( moduleCount );
unsigned long randomModule = rng.lrand32( moduleCount - 1 );
// do some sanity checks
if ( nodeCount < 2 )
{
// no sense in doing anything
return;
}
const std::vector< VertexDescriptorType > allNodesVector
= network->GetVectorOfAllVertexDescriptors();
ToModuleMapType::iterator iter = vertexToModuleMap->find( allNodesVector[ randomNode ] );
const int previousModuleNumber = iter->second;
// if we move the node to its own module, do nothing
if( previousModuleNumber == (long)randomModule )
{
return;
}
iter->second = randomModule;
if( getNumberOfVerticesInModule( vertexToModuleMap, previousModuleNumber ) < 1 )
{
removeModule( vertexToModuleMap, previousModuleNumber );
}
}
void mitk::ConnectomicsSimulatedAnnealingPermutationModularity::splitModule(
ToModuleMapType *vertexToModuleMap, double currentTemperature, mitk::ConnectomicsNetwork::Pointer network, int moduleToSplit )
{
if( m_Depth == 0 )
{
// do nothing
return;
}
// if the module contains only one node, no more division is sensible
if( getNumberOfVerticesInModule( vertexToModuleMap, moduleToSplit ) < 2 )
{
// do nothing
return;
}
// create subgraph of the module, that is to be splitted
mitk::ConnectomicsNetwork::Pointer subNetwork = mitk::ConnectomicsNetwork::New();
VertexToVertexMapType graphToSubgraphVertexMap;
VertexToVertexMapType subgraphToGraphVertexMap;
extractModuleSubgraph( vertexToModuleMap, network, moduleToSplit, subNetwork, &graphToSubgraphVertexMap, &subgraphToGraphVertexMap );
// The submap
ToModuleMapType vertexToModuleSubMap;
// run simulated annealing on the subgraph to determine how the module should be split
if( m_Depth > 0 && m_StepSize > 0 )
{
mitk::ConnectomicsSimulatedAnnealingManager::Pointer manager = mitk::ConnectomicsSimulatedAnnealingManager::New();
mitk::ConnectomicsSimulatedAnnealingPermutationModularity::Pointer permutation = mitk::ConnectomicsSimulatedAnnealingPermutationModularity::New();
mitk::ConnectomicsSimulatedAnnealingCostFunctionModularity::Pointer costFunction = mitk::ConnectomicsSimulatedAnnealingCostFunctionModularity::New();
permutation->SetCostFunction( costFunction.GetPointer() );
permutation->SetNetwork( subNetwork );
permutation->SetDepth( m_Depth - 1 );
permutation->SetStepSize( m_StepSize * 2 );
manager->SetPermutation( permutation.GetPointer() );
manager->RunSimulatedAnnealing( currentTemperature, m_StepSize * 2 );
vertexToModuleSubMap = permutation->GetMapping();
}
// now carry the information over to the original map
std::vector< int > moduleTranslationVector;
moduleTranslationVector.resize( getNumberOfModules( &vertexToModuleSubMap ), 0 );
int originalNumber = getNumberOfModules( vertexToModuleMap );
// the new parts are added at the end
for(unsigned int index( 0 ); index < moduleTranslationVector.size() ; index++)
{
moduleTranslationVector[ index ] = originalNumber + index;
}
ToModuleMapType::iterator iter2 = vertexToModuleSubMap.begin();
ToModuleMapType::iterator end2 = vertexToModuleSubMap.end();
while( iter2 != end2 )
{
// translate vertex descriptor from subgraph to graph
VertexDescriptorType key = subgraphToGraphVertexMap.find( iter2->first )->second;
// translate module number from subgraph to graph
int value = moduleTranslationVector[ iter2->second ];
// change the corresponding entry
vertexToModuleMap->find( key )->second = value;
iter2++;
}
// remove the now empty module, that was splitted
removeModule( vertexToModuleMap, moduleToSplit );
}
double mitk::ConnectomicsSimulatedAnnealingCostFunctionModularity::CalculateModularity( mitk::ConnectomicsNetwork::Pointer network, ToModuleMapType* vertexToModuleMap ) const
{
double modularity( 0.0 );
int numberOfModules = getNumberOfModules( vertexToModuleMap );
if( network->GetNumberOfVertices() != vertexToModuleMap->size() )
{
MBI_ERROR << "Number of vertices and vertex to module map size do not match!";
return modularity;
}
int numberOfLinksInNetwork( 0 );
std::vector< int > numberOfLinksInModule, sumOfDegreesInModule;
numberOfLinksInModule.resize( numberOfModules, 0 );
sumOfDegreesInModule.resize( numberOfModules, 0 );
// get vector of all vertex descriptors in the network
const std::vector< VertexDescriptorType > allNodesVector
= network->GetVectorOfAllVertexDescriptors();
for( int nodeNumber( 0 ); nodeNumber < allNodesVector.size() ; nodeNumber++)
{
int correspondingModule = vertexToModuleMap->find( allNodesVector[ nodeNumber ] )->second;
const std::vector< VertexDescriptorType > adjacentNodexVector
= network->GetVectorOfAdjacentNodes( allNodesVector[ nodeNumber ] );
numberOfLinksInNetwork += adjacentNodexVector.size();
sumOfDegreesInModule[ correspondingModule ] += adjacentNodexVector.size();
for( int adjacentNodeNumber( 0 ); adjacentNodeNumber < adjacentNodexVector.size() ; adjacentNodeNumber++)
{
if( correspondingModule == vertexToModuleMap->find( adjacentNodexVector[ adjacentNodeNumber ] )->second )
{
numberOfLinksInModule[ correspondingModule ]++;
}
}
}
// the numbers for links have to be halved, as each edge was counted twice
numberOfLinksInNetwork = numberOfLinksInNetwork / 2;
// if the network contains no links return 0
if( numberOfLinksInNetwork < 1)
{
return 0;
}
for( int index( 0 ); index < numberOfModules ; index++)
{
numberOfLinksInModule[ index ] = numberOfLinksInModule[ index ] / 2;
}
//Calculate modularity M:
//M = sum_{s=1}^{N_{M}} [ (l_{s} / L) - (d_{s} / ( 2L ))^2 ]
//where N_{M} is the number of modules
//L is the number of links in the network
//l_{s} is the number of links between nodes in the module
//s is the module
//d_{s} is the sum of degrees of the nodes in the module
//( taken from Guimera, R. AND Amaral, L. A. N.
// Cartography of complex networks: modules and universal roles
// Journal of Statistical Mechanics: Theory and Experiment, 2005, 2005, P02001 )
for( int moduleID( 0 ); moduleID < numberOfModules; moduleID++ )
{
modularity += (((double) numberOfLinksInModule[ moduleID ]) / ((double) numberOfLinksInNetwork)) -
(
(((double) sumOfDegreesInModule[ moduleID ]) / ((double) 2 * numberOfLinksInNetwork) ) *
(((double) sumOfDegreesInModule[ moduleID ]) / ((double) 2 * numberOfLinksInNetwork) )
);
}
return modularity;
}