double fitnessDistanceCorrelation(
const std::unordered_map<arma::vec, double, Hash, IsEqual>& samples) {
if (samples.size() < 2) {
throw std::invalid_argument("fitnessDistanceCorrelation: The number of samples must be greater than 2.");
} else if (!isDimensionallyConsistent(samples)) {
throw std::invalid_argument("fitnessDistanceCorrelation: The samples must be dimensionally consistent");
}
// Converts the set of samples into a matrix of parameters (each row is a dimension and each column a parameter) and a row vector of objective values, such that we can use Armadillo C++ to manipulate them.
arma::mat parameters(samples.cbegin()->first.n_elem, samples.size());
arma::rowvec objectiveValues(parameters.n_cols);
arma::uword n = 0;
for (const auto& sample : samples) {
parameters.col(n) = sample.first;
objectiveValues(n) = sample.second;
++n;
}
// Determines one parameter having a minimal objective value within the set of samples.
// The best parameter is then subtracted from all other parameters, so that we can later calculated the distance towards the best one.
arma::uword bestParameterIndex;
objectiveValues.min(bestParameterIndex);
parameters.each_col() -= parameters.col(bestParameterIndex);
// Excludes the best/reference parameter from the correlation, as it will always perfectly correlate with itself and therefore bias the correlation coefficient.
parameters.shed_col(bestParameterIndex);
objectiveValues.shed_col(bestParameterIndex);
// Uses `arma::sum(arma::square(...))` to emulate a column-wise vector norm operator that Armadillo C++ does not have (and this is not likely to change, as it interferes with matrix norms).
return arma::as_scalar(arma::cor(arma::sqrt(arma::sum(arma::square(parameters))), objectiveValues));
}
void FitnessDistanceCorrelationAnalysis::analyseImplementation() {
assert(samples_.size() > 1);
arma::Mat<double> parameters(numberOfDimensions_, samples_.size());
arma::Row<double> objectiveValues(parameters.n_cols);
arma::uword n = 0;
for (const auto& parameterToObjectiveValueMapping : samples_) {
parameters.col(n) = parameterToObjectiveValueMapping.first;
objectiveValues(n) = parameterToObjectiveValueMapping.second;
++n;
}
arma::uword bestParameterIndex;
objectiveValues.min(bestParameterIndex);
parameters.each_col() -= parameters.col(bestParameterIndex);
parameters.shed_col(bestParameterIndex);
objectiveValues.shed_col(bestParameterIndex);
correlationCoefficient_ = arma::as_scalar(arma::cor(arma::sqrt(arma::sum(arma::square(parameters))), objectiveValues));
}