inline const NumericVector * E (const NumericMatrix& mtx){
const NumericVector * rm=rowMeans(mtx);
const NumericVector * jt=jitter(*rm);
delete rm;
return jt;
}
double Mean_Square_Error(NCluster *a, RContext *k, int s, int t){
IOSet *cols = a->GetSetById(s);
IOSet *rows = a->GetSetById(t);
double mse=0;
double allCnt; // cnt of all values in the subspace
double allSum=0; //the sum of all values
double allMean=0;
vector<double> rowMeans(rows->Size());
vector<double> colMeans(cols->Size());
//get row means and total mean
for(int i=0; i < rows->Size();i++){
RSet *lclRow = k->GetSet(t,rows->At(i));
RSet *subSpace = lclRow->GetSubspace(cols);
if(subSpace->Size() > 0){
double sum = subSpace->Sum();
allSum += sum;
allCnt += subSpace->Size();
rowMeans.push_back( sum/(double)cols->Size());
}
delete subSpace;
}
allMean = allSum/allCnt;
//get col means
for(int i=0; i < cols->Size(); i++){
RSet *lclCol = k->GetSet(s,cols->At(i));
RSet *subSpace = lclCol->GetSubspace(rows);
if(subSpace->Size() > 0){
colMeans.push_back(subSpace->Mean());
}
delete subSpace;
}
//now sum for all elements
for(int i=0; i < rows->Size();i++){
RSet *lclRow = k->GetSet(t,rows->At(i));
RSet *subSpace = lclRow->GetSubspace(cols);
if(subSpace->Size() > 0){
for(int j=0; j < subSpace->Size(); j++){
pair<int,double> val = subSpace->At(cols->At(j));
if(val.first != -1)
mse += pow(val.second-rowMeans[j]-colMeans[j]+allMean,2);
}
}
delete subSpace;
}
return mse/allCnt;
}
void PCoA::project(const Matrix& distMatrix)
{
if(distMatrix.size() == 0)
return;
m_projectedData = distMatrix;
// Center squared distance matrix
// Step 1: Square entries and divide by -2.0
for(uint r = 0; r < m_projectedData.size(); ++r)
{
for(uint c = 0; c < m_projectedData.size(); ++c)
{
m_projectedData[r][c] = m_projectedData.at(r).at(c)*m_projectedData.at(r).at(c) / -2.0;
}
}
// Step 2: Calculate column and row means
std::vector<double> colMeans(m_projectedData.size(), 0);
std::vector<double> rowMeans(m_projectedData.size(), 0);
for(uint r = 0; r < m_projectedData.size(); ++r)
{
for(uint c = 0; c < m_projectedData.size(); ++c)
{
rowMeans[r] += m_projectedData.at(r).at(c);
colMeans[c] += m_projectedData.at(r).at(c);
}
}
for(uint i = 0; i < m_projectedData.size(); ++i)
{
rowMeans[i] /= m_projectedData.size();
colMeans[i] /= m_projectedData.size();
}
// Step 3: Calculate matrix mean
double matrixMean = 0;
for(uint i = 0; i < m_projectedData.size(); ++i)
matrixMean += rowMeans.at(i);
matrixMean /= m_projectedData.size();
// Step 4: Calculate actual "centered" distance matrix
for(uint r = 0; r < m_projectedData.size(); ++r)
{
for(uint c = 0; c < m_projectedData.size(); ++c)
{
m_projectedData[r][c] = m_projectedData.at(r).at(c) - rowMeans.at(r) - colMeans.at(c) + matrixMean;
}
}
// Step 5: Calculate eigenvectors and eigenvalues
double* M = new double[m_projectedData.size() * m_projectedData.size()]; // input matrix
double* U = new double[m_projectedData.size() * m_projectedData.size()]; // eigenvectors
double* D = new double[m_projectedData.size()]; // real component of eigenvalues
double* E = new double[m_projectedData.size()]; // imaginary component of eigenvalues
for(uint r = 0; r < m_projectedData.size(); ++r)
{
for(uint c = 0; c < m_projectedData.size(); ++c)
{
M[c+r*m_projectedData.size()] = m_projectedData.at(r).at(c);
}
}
EigDecomp(M, U, D, E, m_projectedData.size());
// Step 6: Find desending order of eigenvalues
for(uint i = 0; i < m_projectedData.size(); ++i)
D[i] = fabs(D[i]);
m_eigenValues.clear();
m_sumEigenvalues = 0;
for(uint i = 0; i < m_projectedData.size(); ++i)
{
m_sumEigenvalues += D[i];
m_eigenValues.push_back(D[i]);
}
std::sort(m_eigenValues.begin(), m_eigenValues.end(), std::greater<double>());
std::vector<uint> indexOrder;
for(uint i = 0; i < m_projectedData.size(); ++i)
{
bool bBreak = false;
for(uint j = 0; j < m_projectedData.size() && !bBreak; ++j)
{
if(m_eigenValues.at(i) == D[j])
{
indexOrder.push_back(j);
bBreak = true;
}
}
}
// Step 7: Calculate variance and summed variance for each embedded dimension
m_variance.clear();
m_sumVariance.clear();
for(uint i = 0; i < m_projectedData.size(); ++i)
{
m_variance.push_back(m_eigenValues.at(i) / m_sumEigenvalues);
if(i == 0)
m_sumVariance.push_back(m_variance.at(0));
else
m_sumVariance.push_back(m_sumVariance.at(i-1) + m_variance.at(i));
}
// Step 8: Transform eigenvector matrix into new embedded space
for(uint i = 0; i < m_projectedData.size(); ++i)
{
D[i] = sqrt(D[i]);
for(uint r = 0; r < m_projectedData.size(); ++r)
{
for(uint c = 0; c < m_projectedData.size(); ++c)
{
m_projectedData[r][c] = U[indexOrder.at(c)+r*m_projectedData.size()]*D[indexOrder.at(c)];
}
}
}
delete[] M;
delete[] U;
delete[] D;
delete[] E;
}
