void EMFit<InitialClusteringType, CovarianceConstraintPolicy>::Estimate(
const arma::mat& observations,
std::vector<arma::vec>& means,
std::vector<arma::mat>& covariances,
arma::vec& weights,
const bool useInitialModel)
{
// Only perform initial clustering if the user wanted it.
if (!useInitialModel)
InitialClustering(observations, means, covariances, weights);
double l = LogLikelihood(observations, means, covariances, weights);
Log::Debug << "EMFit::Estimate(): initial clustering log-likelihood: "
<< l << std::endl;
double lOld = -DBL_MAX;
arma::mat condProb(observations.n_cols, means.size());
// Iterate to update the model until no more improvement is found.
size_t iteration = 1;
while (std::abs(l - lOld) > tolerance && iteration != maxIterations)
{
Log::Info << "EMFit::Estimate(): iteration " << iteration << ", "
<< "log-likelihood " << l << "." << std::endl;
// Calculate the conditional probabilities of choosing a particular
// Gaussian given the observations and the present theta value.
for (size_t i = 0; i < means.size(); i++)
{
// Store conditional probabilities into condProb vector for each
// Gaussian. First we make an alias of the condProb vector.
arma::vec condProbAlias = condProb.unsafe_col(i);
phi(observations, means[i], covariances[i], condProbAlias);
condProbAlias *= weights[i];
}
// Normalize row-wise.
for (size_t i = 0; i < condProb.n_rows; i++)
{
// Avoid dividing by zero; if the probability for everything is 0, we
// don't want to make it NaN.
const double probSum = accu(condProb.row(i));
if (probSum != 0.0)
condProb.row(i) /= probSum;
}
// Store the sum of the probability of each state over all the observations.
arma::vec probRowSums = trans(arma::sum(condProb, 0 /* columnwise */));
// Calculate the new value of the means using the updated conditional
// probabilities.
for (size_t i = 0; i < means.size(); i++)
{
// Don't update if there's no probability of the Gaussian having points.
if (probRowSums[i] != 0)
means[i] = (observations * condProb.col(i)) / probRowSums[i];
// Calculate the new value of the covariances using the updated
// conditional probabilities and the updated means.
arma::mat tmp = observations - (means[i] *
arma::ones<arma::rowvec>(observations.n_cols));
arma::mat tmpB = tmp % (arma::ones<arma::vec>(observations.n_rows) *
trans(condProb.col(i)));
// Don't update if there's no probability of the Gaussian having points.
if (probRowSums[i] != 0.0)
covariances[i] = (tmp * trans(tmpB)) / probRowSums[i];
// Apply covariance constraint.
constraint.ApplyConstraint(covariances[i]);
}
// Calculate the new values for omega using the updated conditional
// probabilities.
weights = probRowSums / observations.n_cols;
// Update values of l; calculate new log-likelihood.
lOld = l;
l = LogLikelihood(observations, means, covariances, weights);
iteration++;
}
}
void EMFit<InitialClusteringType>::Estimate(const arma::mat& observations,
const arma::vec& probabilities,
std::vector<arma::vec>& means,
std::vector<arma::mat>& covariances,
arma::vec& weights)
{
InitialClustering(observations, means, covariances, weights);
double l = LogLikelihood(observations, means, covariances, weights);
Log::Debug << "EMFit::Estimate(): initial clustering log-likelihood: "
<< l << std::endl;
double lOld = -DBL_MAX;
arma::mat condProb(observations.n_cols, means.size());
// Iterate to update the model until no more improvement is found.
size_t iteration = 1;
while (std::abs(l - lOld) > tolerance && iteration != maxIterations)
{
// Calculate the conditional probabilities of choosing a particular
// Gaussian given the observations and the present theta value.
for (size_t i = 0; i < means.size(); i++)
{
// Store conditional probabilities into condProb vector for each
// Gaussian. First we make an alias of the condProb vector.
arma::vec condProbAlias = condProb.unsafe_col(i);
phi(observations, means[i], covariances[i], condProbAlias);
condProbAlias *= weights[i];
}
// Normalize row-wise.
for (size_t i = 0; i < condProb.n_rows; i++)
{
// Avoid dividing by zero; if the probability for everything is 0, we
// don't want to make it NaN.
const double probSum = accu(condProb.row(i));
if (probSum != 0.0)
condProb.row(i) /= probSum;
}
// This will store the sum of probabilities of each state over all the
// observations.
arma::vec probRowSums(means.size());
// Calculate the new value of the means using the updated conditional
// probabilities.
for (size_t i = 0; i < means.size(); i++)
{
// Calculate the sum of probabilities of points, which is the
// conditional probability of each point being from Gaussian i
// multiplied by the probability of the point being from this mixture
// model.
probRowSums[i] = accu(condProb.col(i) % probabilities);
means[i] = (observations * (condProb.col(i) % probabilities)) /
probRowSums[i];
// Calculate the new value of the covariances using the updated
// conditional probabilities and the updated means.
arma::mat tmp = observations - (means[i] *
arma::ones<arma::rowvec>(observations.n_cols));
arma::mat tmpB = tmp % (arma::ones<arma::vec>(observations.n_rows) *
trans(condProb.col(i) % probabilities));
covariances[i] = (tmp * trans(tmpB)) / probRowSums[i];
// Ensure positive-definiteness. TODO: make this more efficient.
if (forcePositive && det(covariances[i]) <= 1e-50)
{
Log::Debug << "Covariance matrix " << i << " is not positive definite. "
<< "Adding perturbation." << std::endl;
double perturbation = 1e-30;
while (det(covariances[i]) <= 1e-50)
{
covariances[i].diag() += perturbation;
perturbation *= 10; // Slow, but we don't want to add too much.
}
}
}
// Calculate the new values for omega using the updated conditional
// probabilities.
weights = probRowSums / accu(probabilities);
// Update values of l; calculate new log-likelihood.
lOld = l;
l = LogLikelihood(observations, means, covariances, weights);
iteration++;
}
}