//! Returns a model mapping encoded data from the
//! m-dimensional PCA coordinate system back to the
//! n-dimensional original coordinate system.
void PCA::decoder(LinearModel<>& model, std::size_t m) {
if(!m) m = std::min(m_n,m_l);
if( m == m_n && !m_whitening){
model.setStructure(m_eigenvectors, m_mean);
}
RealMatrix A = columns(m_eigenvectors, 0, m);
if(m_whitening){
for(std::size_t i=0; i<A.size2(); i++) {
//take care of numerical difficulties for very small eigenvalues.
if(m_eigenvalues(i)/m_eigenvalues(0) < 1.e-15){
column(A,i).clear();
}
else{
column(A, i) = column(A, i) * std::sqrt(m_eigenvalues(i));
}
}
}
model.setStructure(A, m_mean);
}
void LinearRegression::train(LinearModel<>& model, LabeledData<RealVector, RealVector> const& dataset){
std::size_t inputDim = inputDimension(dataset);
std::size_t outputDim = labelDimension(dataset);
std::size_t numInputs = dataset.numberOfElements();
std::size_t numBatches = dataset.numberOfBatches();
//Let P be the matrix of points with n rows and X=(P|1). the 1 rpresents the bias weight
//Let A = X^T X + lambda * I
//than whe have (for lambda = 0)
//A = ( P^T P P^T 1)
// ( 1^T P 1^T1)
RealMatrix matA(inputDim+1,inputDim+1,0.0);
blas::Blocking<RealMatrix> Ablocks(matA,inputDim,inputDim);
//compute A and the label matrix batchwise
typedef LabeledData<RealVector, RealVector>::const_batch_reference BatchRef;
for (std::size_t b=0; b != numBatches; b++){
BatchRef batch = dataset.batch(b);
symm_prod(trans(batch.input),Ablocks.upperLeft(),false);
noalias(column(Ablocks.upperRight(),0))+=sum_rows(batch.input);
}
row(Ablocks.lowerLeft(),0) = column(Ablocks.upperRight(),0);
matA(inputDim,inputDim) = numInputs;
//X^TX+=lambda* I
diag(Ablocks.upperLeft())+= blas::repeat(m_regularization,inputDim);
//we also need to compute X^T L= (P^TL, 1^T L) where L is the matrix of labels
RealMatrix XTL(inputDim + 1,outputDim,0.0);
for (std::size_t b=0; b != numBatches; b++){
BatchRef batch = dataset.batch(b);
RealSubMatrix PTL = subrange(XTL,0,inputDim,0,outputDim);
axpy_prod(trans(batch.input),batch.label,PTL,false);
noalias(row(XTL,inputDim))+=sum_rows(batch.label);
}
//we solve the system A Beta = X^T L
//usually this is solved via the moore penrose inverse:
//Beta = A^-1 T
//but it is faster und numerically more stable, if we solve it as a symmetric system
//w can use in-place solve
RealMatrix& beta = XTL;
blas::solveSymmSemiDefiniteSystemInPlace<blas::SolveAXB>(matA,beta);
RealMatrix matrix = subrange(trans(beta), 0, outputDim, 0, inputDim);
RealVector offset = row(beta,inputDim);
// write parameters into the model
model.setStructure(matrix, offset);
}
//! Returns a model mapping the original data to the
//! m-dimensional PCA coordinate system.
void PCA::encoder(LinearModel<>& model, std::size_t m) {
if(!m) m = std::min(m_n,m_l);
RealMatrix A = trans(columns(m_eigenvectors, 0, m) );
RealVector offset = -prod(A, m_mean);
if(m_whitening){
for(std::size_t i=0; i<A.size1(); i++) {
//take care of numerical difficulties for very small eigenvalues.
if(m_eigenvalues(i)/m_eigenvalues(0) < 1.e-15){
row(A,i).clear();
offset(i) = 0;
}
else{
row(A, i) /= std::sqrt(m_eigenvalues(i));
offset(i) /= std::sqrt(m_eigenvalues(i));
}
}
}
model.setStructure(A, offset);
}
// optimize the sigmoid using rprop on the negative log-likelihood
void SigmoidFitRpropNLL::train(SigmoidModel& model, LabeledData<RealVector, unsigned int> const& dataset)
{
LinearModel<> trainModel;
trainModel.setStructure(1,1,model.hasOffset());
CrossEntropy loss;
ErrorFunction modeling_error( dataset, &trainModel, &loss );
IRpropPlus rprop;
rprop.init( modeling_error );
for (unsigned int i=0; i<m_iterations; i++) {
rprop.step( modeling_error );
}
RealVector solution(2,0.0);
solution(0) = rprop.solution().point(0);
if(model.slopeIsExpEncoded()){
solution(0) = std::log(solution(0));
}
if(model.hasOffset())
solution(1) =-rprop.solution().point(1);
model.setParameterVector(solution);
}