/** recompute cluster membership as well as eigen systems for each
cluster */
void
KMeansClustering::recomputeClusterStats( unsigned stats )
{
unsigned long i, j;
// recompute the eigen systems if required
if( clusterStatsValid< stats && stats> 0 )
{
// update cluster memberships
unsigned long numPoints= data->data.size();
for( i= 0 ; i< numClusters ; i++ )
clusters[i].memberCount= 0;
for( i= 0 ; i< numPoints ; i++ )
{
j= bestCluster( data->data[i] );
clusterIDs[i]= j;
clusters[j].memberCount++;
}
// compute covariance matrices
Vector h( data->data[0].getSize() );
for( i= 0 ; i< numClusters ; i++ )
clusters[i].cov.zero();
for( i= 0 ; i< numPoints ; i++ )
{
h.copy( data->data[i] );
h-= clusters[clusterIDs[i]].mean;
clusters[clusterIDs[i]].cov.addOuterProduct( h );
}
for( i= 0 ; i< numClusters ; i++ )
clusters[i].cov/= (double)clusters[i].memberCount;
// compute eigen vectors, eigen values
JacobiRotation solver;
for( i= 0 ; i< numClusters ; i++ )
solver.solve( clusters[i].cov, clusters[i].eigenValues,
clusters[i].eigenVectors );
clusterStatsValid= 1;
}
// if necessary, restore upper triangle of covariance matrices
// (may have been destroyed by eigensolver)
if( clusterStatsValid< 2 && stats>= 2 )
{
unsigned dim= data->data[0].getSize();
for( unsigned k= 0 ; k< numClusters ; k++ )
{
Matrix &m= clusters[k].cov;
for( i= 0 ; i< dim ; i++ )
for( j= i+1 ; j< dim ; j++ )
m[j][i]= m[i][j];
}
clusterStatsValid= 2;
}
}
int main(int, char**)
{
cout.precision(3);
Vector2f v = Vector2f::Random();
JacobiRotation<float> G;
G.makeGivens(v.x(), v.y());
cout << "Here is the vector v:" << endl << v << endl;
v.applyOnTheLeft(0, 1, G.adjoint());
cout << "Here is the vector J' * v:" << endl << v << endl;
return 0;
}
int main(int, char**)
{
cout.precision(3);
Matrix2f m = Matrix2f::Random();
m = (m + m.adjoint()).eval();
JacobiRotation<float> J;
J.makeJacobi(m, 0, 1);
cout << "Here is the matrix m:" << endl << m << endl;
m.applyOnTheLeft(0, 1, J.adjoint());
m.applyOnTheRight(0, 1, J);
cout << "Here is the matrix J' * m * J:" << endl << m << endl;
return 0;
}
/** split a specific cluster along its largest eigenvector */
void
KMeansClustering::splitCluster( unsigned cluster )
{
unsigned long i;
// recompute eigen systems if necessary
if( clusterStatsValid< 1 )
recomputeClusterStats( 1 );
// split the current mean into two along the largest eigenvector
unsigned dimension= data->data[0].getSize();
clusters.push_back( clusters[cluster] ); // copy mean to new cluster
ClusterStats *c1= &(clusters[cluster]);
ClusterStats *c2= &(clusters[numClusters]);
c1->mean.addScalarTimesVector( c1->eigenValues[0], c1->eigenVectors[0] );
c2->mean.addScalarTimesVector( -c1->eigenValues[0], c1->eigenVectors[0] );
// update the cluster membership only for members of the origonal cluster
unsigned long numPoints= data->data.size();
for( i= 0 ; i< numPoints ; i++ )
if( clusterIDs[i]== cluster )
if( dist( data->data[i], c2->mean )< dist( data->data[i], c1->mean ) )
clusterIDs[i]= numClusters;
// update the two means to actually be the means of the respective
// point cluster
c1->mean.zero();
c2->mean.zero();
c1->memberCount= c2->memberCount= 0;
for( i= 0 ; i< numPoints ; i++ )
{
if( clusterIDs[i]== cluster )
{
c1->mean+= data->data[i];
c1->memberCount++;
}
if( clusterIDs[i]== numClusters )
{
c2->mean+= data->data[i];
c2->memberCount++;
}
}
c1->mean/= (double)c1->memberCount;
c2->mean/= (double)c2->memberCount;
// update the two convariance matrices;
Vector h( data->data[0].getSize() );
c1->cov.zero();
c2->cov.zero();
for( i= 0 ; i< numPoints ; i++ )
{
if( clusterIDs[i]== cluster )
{
h.copy( data->data[i] );
h-= c1->mean;
c1->cov.addOuterProduct( h );
}
if( clusterIDs[i]== numClusters )
{
h.copy( data->data[i] );
h-= c2->mean;
c2->cov.addOuterProduct( h );
}
}
c1->cov/= (double)c1->memberCount;
c2->cov/= (double)c2->memberCount;
// recompute eigen values, eigen vectors
JacobiRotation solver;
solver.solve( c1->cov, c1->eigenValues, c1->eigenVectors );
solver.solve( c2->cov, c2->eigenValues, c2->eigenVectors );
// we have one more cluster now
numClusters++;
}
/** merge two specified clusters */
void
KMeansClustering::mergeClusters( unsigned c1, unsigned c2 )
{
unsigned long i, j;
// make sure c1 is the cluster with the smaller ID
if( c1> c2 )
{
i= c1; c1= c2; c2=i;
}
/*
cerr << "Before:\n";
for( i= 0 ; i< numClusters ; i++ )
{
for( j= 0 ; j< clusters[i].mean.getSize() ; j++ )
cerr << ' ' << clusters[i].eigenValues[j];
cerr << "\t\t" << clusters[i].memberCount << endl;
}
*/
// new mean is old means weighted by memeber counts
double w= clusters[c1].memberCount;
clusters[c1].memberCount+= clusters[c2].memberCount;
w/= clusters[c1].memberCount;
clusters[c1].mean*= w;
clusters[c1].mean.addScalarTimesVector( 1.0-w, clusters[c2].mean );
// update cluster membership, covariance matrix, eigenvalues of c1
// (only if these quantities are valid for the other clusters)
if( clusterStatsValid> 0 )
{
// covariance matrix
unsigned long numPoints= data->data.size();
Vector h( data->data[0].getSize() );
clusters[c1].cov.zero();
for( i= 0 ; i< numPoints ; i++ )
{
// merge merge all points from c2 into c1
if( clusterIDs[i]== c2 )
clusterIDs[i]= c1;
if( clusterIDs[i]== c1 )
{
h.copy( data->data[i] );
h-= clusters[c1].mean;
clusters[c1].cov.addOuterProduct( h );
}
// the cluster indices > c2 are now reduced by one
if( clusterIDs[i]> c2 )
clusterIDs[i]--;
}
clusters[c1].cov/= clusters[c1].memberCount;
// eigenvalues and eigenvectors
JacobiRotation solver;
solver.solve( clusters[c1].cov, clusters[c1].eigenValues,
clusters[c1].eigenVectors );
}
// consolidate array
numClusters--;
for( i= c2 ; i< numClusters ; i++ )
clusters[i].copy( clusters[i+1] );
clusters.pop_back();
/*
cerr << "After:\n";
for( i= 0 ; i< numClusters ; i++ )
{
for( j= 0 ; j< clusters[i].mean.getSize() ; j++ )
cerr << ' ' << clusters[i].eigenValues[j];
cerr << "\t\t" << clusters[i].memberCount << endl;
}
*/
}
/** fit a line to a SampleVector of data-points */
void fitToDataPoints( Line &l, const SampleVector &dataPoints )
{
// The least squares line goes through the mean of all points
// and the direction is the first eigenvector of the co-variance
// matrix of the points
//Exit if datapoints empty
if( dataPoints.data.size() == 0 )
return;
// First, compute arithmetic mean
unsigned long dimension = l.p1.getSize();
Vector mean(dimension, 0.0);
for( unsigned long i = 0; i < dataPoints.data.size(); i++ )
{
//Exit if wrong size
if( dataPoints.data.at(i).getSize() != l.p1.getSize() )
{
cerr << "Vector dimensions must match! " << std::endl;
return;
}
mean += dataPoints.data.at(i);
}
mean /= (double)dataPoints.data.size();
// Compute covariance-matrix
Matrix cov( dimension, dimension, true );
Vector covEntry(dimension, 0.0);
for( unsigned long i = 0 ; i< dataPoints.data.size() ; i++ )
{
covEntry.copy( dataPoints.data.at(i) );
covEntry -= mean;
cov.addOuterProduct( covEntry );
}
// Solve Eigenvalue problem
JacobiRotation solver;
Vector eigValues( dimension, 0.0 );
Matrix eigVectors( dimension, dimension, true);
solver.solve( cov, eigValues, eigVectors );
// Find the eigenVector with the larges eigenValue
unsigned long largestEigenVector = 0;
for( unsigned long i = 0; i < dimension; i++ )
{
if( eigValues[i] > eigValues[largestEigenVector] )
largestEigenVector = i;
}
// Direction of the line is then
Vector direction(dimension, 0.0);
direction.assign( eigVectors.getRowVector(largestEigenVector) );
// Store in 2-point representation
l.p1.assign( mean );
l.p2.assign( mean );
l.p2 += direction;
return;
}