positive_definite_constraint.hpp

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#ifndef MLPACK_METHODS_GMM_POSITIVE_DEFINITE_CONSTRAINT_HPP
#define MLPACK_METHODS_GMM_POSITIVE_DEFINITE_CONSTRAINT_HPP

#include <mlpack/prereqs.hpp>

namespace mlpack {
namespace gmm {

class PositiveDefiniteConstraint
{
 public:
  static void ApplyConstraint(arma::mat& covariance)
  {
    // What we want to do is make sure that the matrix is positive definite and
    // that the condition number isn't too large.  We also need to ensure that
    // the covariance matrix is not too close to zero (hence, we ensure that all
    // eigenvalues are at least 1e-50).
    arma::vec eigval;
    arma::mat eigvec;
    arma::eig_sym(eigval, eigvec, covariance);

    // If the matrix is not positive definite or if the condition number is
    // large, we must project it back onto the cone of positive definite
    // matrices with reasonable condition number (I'm picking 1e5 here, not for
    // any particular reason).
    if ((eigval[0] < 0.0) || ((eigval[eigval.n_elem - 1] / eigval[0]) > 1e5) ||
        (eigval[eigval.n_elem - 1] < 1e-50))
    {
      // Project any negative eigenvalues back to non-negative, and project any
      // too-small eigenvalues to a large enough value.  Make them as small as
      // possible to satisfy our constraint on the condition number.
      const double minEigval = std::max(eigval[eigval.n_elem - 1] / 1e5, 1e-50);
      for (size_t i = 0; i < eigval.n_elem; ++i)
        eigval[i] = std::max(eigval[i], minEigval);

      // Now reassemble the covariance matrix.
      covariance = eigvec * arma::diagmat(eigval) * eigvec.t();
    }
  }

  static void ApplyConstraint(arma::vec& diagCovariance)
  {
    // If the matrix is not positive definite or if the condition number is
    // large, we must project it back onto the cone of positive definite
    // matrices with reasonable condition number (I'm picking 1e5 here, not for
    // any particular reason).
    double maxEigval = -DBL_MAX;
    for (size_t i = 0; i < diagCovariance.n_elem; ++i)
    {
      if (diagCovariance[i] > maxEigval)
        maxEigval = diagCovariance[i];
    }

    for (size_t i = 0; i < diagCovariance.n_elem; ++i)
    {
      if ((diagCovariance[i] < 0.0) || ((maxEigval / diagCovariance[i]) > 1e5)
          || (maxEigval < 1e-50))
      {
        diagCovariance[i] = std::max(maxEigval / 1e5, 1e-50);
      }
    }
  }

  template<typename Archive>
  static void serialize(Archive& /* ar */, const unsigned int /* version */) { }
};

} // namespace gmm
} // namespace mlpack

#endif