GMMExpectationMaximization::uint GMMExpectationMaximization::execute(const MatrixX & dataset)
{
const uint data_count = dataset.rows();
const uint num_gaussians = m_means.size();
const uint dim = dataset.cols();
MatrixX pxi(data_count,num_gaussians);
MatrixX pix(data_count,num_gaussians);
VectorX pxidatatot(data_count);
VectorX weights(num_gaussians);
VectorX ex(data_count);
MatrixX ts(dim,dim);
VectorX dif(dim);
Real prev_log_likelyhood = 1.0;
uint it_num;
for (it_num = 0; it_num < m_max_iterations; it_num++)
{
for (uint g = 0; g < num_gaussians; g++)
weights[g] = m_weights[g];
for (uint d = 0; d < data_count; d++)
for (uint g = 0; g < num_gaussians; g++)
pxi(d,g) = gauss(m_means[g],m_covs[g],dataset.row(d).transpose());
pxidatatot = pxi * weights;
Real log_likelyhood = pxidatatot.array().log().sum() / Real(data_count);
if (it_num != 0 && (std::abs(log_likelyhood / prev_log_likelyhood - 1.0) < m_termination_threshold))
break;
prev_log_likelyhood = log_likelyhood;
for (uint d = 0; d < data_count; d++)
pix.row(d) = (pxi.row(d).transpose().array() * weights.array()).transpose() / pxidatatot[d];
ex = pix.colwise().sum();
for(uint g = 0; g < num_gaussians; g++)
{
m_weights[g] = ex[g] / Real(data_count);
m_means[g] = (dataset.transpose() * pix.col(g)) / ex[g];
ts = MatrixX::Zero(dim,dim);
for (uint d = 0; d < data_count; d++)
{
dif = dataset.row(d).transpose() - m_means[g];
ts.noalias() += (dif * dif.transpose()) * pix(d,g);
}
m_covs[g] = (ts / ex[g]) + MatrixX::Identity(dim,dim) * m_epsilon;
}
// interruption point here
if (m_termination_handler && m_termination_handler->isTerminated())
return it_num;
}
return it_num;
}
void run_test(int dim, int num_elements)
{
using std::abs;
typedef typename internal::traits<MatrixType>::Scalar Scalar;
typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
// MUST be positive because in any other case det(cR_t) may become negative for
// odd dimensions!
const Scalar c = abs(internal::random<Scalar>());
MatrixX R = randMatrixSpecialUnitary<Scalar>(dim);
VectorX t = Scalar(50)*VectorX::Random(dim,1);
MatrixX cR_t = MatrixX::Identity(dim+1,dim+1);
cR_t.block(0,0,dim,dim) = c*R;
cR_t.block(0,dim,dim,1) = t;
MatrixX src = MatrixX::Random(dim+1, num_elements);
src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
MatrixX dst = cR_t*src;
MatrixX cR_t_umeyama = umeyama(src.block(0,0,dim,num_elements), dst.block(0,0,dim,num_elements));
const Scalar error = ( cR_t_umeyama*src - dst ).norm() / dst.norm();
VERIFY(error < Scalar(40)*std::numeric_limits<Scalar>::epsilon());
}
void run_fixed_size_test(int num_elements)
{
using std::abs;
typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX;
typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix;
typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix;
typedef Matrix<Scalar, Dimension, 1> FixedVector;
const int dim = Dimension;
// MUST be positive because in any other case det(cR_t) may become negative for
// odd dimensions!
const Scalar c = abs(internal::random<Scalar>());
FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim);
FixedVector t = Scalar(50)*FixedVector::Random(dim,1);
HomMatrix cR_t = HomMatrix::Identity(dim+1,dim+1);
cR_t.block(0,0,dim,dim) = c*R;
cR_t.block(0,dim,dim,1) = t;
MatrixX src = MatrixX::Random(dim+1, num_elements);
src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
MatrixX dst = cR_t*src;
Block<MatrixX, Dimension, Dynamic> src_block(src,0,0,dim,num_elements);
Block<MatrixX, Dimension, Dynamic> dst_block(dst,0,0,dim,num_elements);
HomMatrix cR_t_umeyama = umeyama(src_block, dst_block);
const Scalar error = ( cR_t_umeyama*src - dst ).array().square().sum();
VERIFY(error < Scalar(10)*std::numeric_limits<Scalar>::epsilon());
}
GMMExpectationMaximization::Real GMMExpectationMaximization::getBIC(const MatrixX & dataset) const
{
const uint dim = dataset.cols();
const uint num_gaussians = m_means.size();
Real number_of_parameters = (num_gaussians * dim * (dim + 1) / 2) + num_gaussians * dim + num_gaussians - 1;
uint data_count = dataset.rows();
Real sum = 0.0;
for(uint i = 0; i < data_count; i++)
sum += log(expectation(dataset.row(i).transpose()));
return -sum + (number_of_parameters / 2.0) * log(Real(data_count));
}
void GMMExpectationMaximization::autoInitializeByEqualIntervals(uint num_gaussians,uint col,const MatrixX & dataset)
{
uint data_count = dataset.rows();
uint dim = dataset.cols();
std::vector<std::vector<uint> > index(num_gaussians);
for(uint g = 0; g < num_gaussians; g++)
index[g].reserve(data_count / num_gaussians);
m_weights.clear();
m_weights.resize(num_gaussians);
m_means.clear();
m_means.resize(num_gaussians,VectorX::Zero(dim));
m_covs.clear();
m_covs.resize(num_gaussians,MatrixX::Zero(dim,dim));
// find max and min value for column col
Real cmax = dataset(0,col);
Real cmin = dataset(0,col);
for(uint n = 1; n < data_count; n++)
{
if (dataset(n,col) > cmax) cmax = dataset(n,col);
if (dataset(n,col) < cmin) cmin = dataset(n,col);
}
Real cspan = cmax - cmin;
for(uint n = 0; n < data_count; n++)
{
// compute gaussian index to which this point belongs
uint gi = uint((dataset(n,col) - cmin) / (cspan + 1.0) * Real(num_gaussians));
// sum the points to obtain means
m_means[gi] += dataset.row(n);
index[gi].push_back(n);
}
for (uint g = 0; g < num_gaussians; g++)
{
uint popsize = index[g].size();
// avoid division by zero: if no samples are available, initialize to something from somewhere
if (popsize == 0)
{
m_means[g] = dataset.row(g % data_count);
m_covs[g] = MatrixX::Identity(dim,dim);
m_weights[g] = 1.0f / Real(num_gaussians);
continue;
}
// average by popsize
m_means[g] /= Real(popsize);
// same weight for all gaussians
m_weights[g] = 1.0f / Real(num_gaussians);
// compute covariance matrix
for (uint p = 0; p < popsize; p++)
{
const Eigen::VectorXf & r = dataset.row(index[g][p]);
const Eigen::VectorXf & m = m_means[g];
m_covs[g] += (r - m) * (r - m).transpose();
}
m_covs[g] /= Real(popsize);
m_covs[g] += MatrixX::Identity(dim,dim) * m_epsilon;
}
}