double Cpoint3dCov::mahalanobisDistance(const Cpoint3d &qq) const
{
double dm2;
Vector3f vDiff, vAux;
vDiff << ( this->xx - qq.getX() ), ( this->yy - qq.getY() ), ( this->zz - qq.getZ() );//difference vector
vAux = covMat.inverse()*vDiff;
dm2 = vDiff(0)*vAux(0) + vDiff(1)*vAux(1) + vDiff(2)*vAux(2);
return sqrt(dm2);
}
double Cpoint3dCov::mahalanobisDistance2D(const Cpoint3d &qq) const
{
double dm2;
Vector2f vDiff, vAux;
vDiff << ( this->xx - qq.getX() ), ( this->yy - qq.getY() );//difference vector
vAux = (covMat.block<2,2>(0,0).inverse())*vDiff;
dm2 = vDiff(0)*vAux(0) + vDiff(1)*vAux(1);
return sqrt(dm2);
}
// estimate the feature transform for the given data (typically speaker adaptation data)
Transform *FMLLREstimator::estimateTransform(Transform *transformInitial) {
Matrix<double> matrixW(m_iDim,m_iDim+1);
Matrix<float> matrixWF(m_iDim,m_iDim+1);
Matrix<double> matrixA(m_iDim,m_iDim);
Vector<double> vAux(m_iDim+1);
// starting from scratch: bias = 0.0 and A = identity
if (transformInitial == NULL) {
matrixA.setIdentity();
}
// starting from another transform
else {
assert(0);
}
// compute the matrix of cofactors of A
Matrix<double> matrixP(matrixA);
matrixP.matrixCofactor();
// initialize the transform
// iterative update
for(int iIteration = 0 ; iIteration < m_iIterations ; ++iIteration) {
// compute the transform row by row
for(int i=0 ; i < m_iDim ; ++i) {
// invert G(i) (this is suboptimal, the inversion needs to be
// done just once then it can be reused across iterations)
Matrix<double> matrixGInverted(*m_matrixG[i]);
matrixGInverted.invert();
// compute alpha (it implies solving a quadratic equation and selecting the solution
// that produces a higher increase of the objective function)
// get the zero extended vector of cofactors for the ith row
Vector<double> vCofactor(matrixP.getRow(i));
vCofactor.appendFront(0.0);
// compute constants
double dBeta = m_fOccupancyTotal;
Vector<double> vAux(m_iDim+1);
vAux.mul(vCofactor,matrixGInverted);
double dA = vAux.mul(vCofactor);
double dB = vAux.mul(m_matrixK->getRow(i));
double dC = -1.0*dBeta;
// there are two possible solutions
double dAlpha1 = (-1.0*dB + sqrt(dB*dB - 4.0*dA*dC))/(2.0*dA);
double dAlpha2 = (-1.0*dB - sqrt(dB*dB - 4.0*dA*dC))/(2.0*dA);
// we let the objective function decide which solution is better (higher likelihood increase)
double dAuxiliarFunction1 = dBeta*log(fabs(dAlpha1*dA+dB)) - 0.5*dAlpha1*dAlpha1*dA;
double dAuxiliarFunction2 = dBeta*log(fabs(dAlpha2*dA+dB)) - 0.5*dAlpha2*dAlpha2*dA;
double dAlpha = (dAuxiliarFunction1 > dAuxiliarFunction2) ? dAlpha1 : dAlpha2;
// compute the w(i)
Vector<double> vAux2(m_matrixK->getRow(i));
Vector<double> vCofactorRowEx(matrixP.getRow(i));
vCofactorRowEx.appendFront(0.0);
vAux2.add(dAlpha,vCofactorRowEx);
matrixW.getRow(i).mul(vAux2,matrixGInverted);
// update A
matrixA.getRow(i).copy(matrixW.getRowData(i)+1,m_iDim);
// compute the matrix of cofactors after updating the row of the transform
matrixP.copy(matrixA);
matrixP.matrixCofactor();
}
// compute the log(|A|)
Matrix<double> matrixAInverted(matrixA);
float fDet = (float)matrixAInverted.invert();
if (fDet == 0) {
BVC_ERROR << "the A matrix is singular!, can't compute inverse";
}
printf("log(|A|) = %8.4f\n",log(fDet));
}
// create the transform
Matrix<float> matrixWFloat(matrixW);
return new Transform(TRANSFORM_TYPE_AFFINE,matrixWFloat);
}
