fit_ellipsoid()

EllipsoidExtent MayaFlux::Kinesis::fit_ellipsoid ( std::span< const Eigen::VectorXd >  samples, double  radius_sigma = 2.0, double  softness = 0.5  )

inline

Fit an ellipsoid extent from the mean and spread of a sample set.

Parameters

samples	Observations, all of the same dimension
radius_sigma	Per-axis radius as a multiple of that axis's standard deviation
softness	Additional normalized distance over which membership falls to zero beyond the fitted radius

Returns

Centre at the sample mean, radii at radius_sigma standard deviations

The prototype form of a demonstrated meaning: the centre is what was done on average and the radii are how much it varied, so an axis held consistently across demonstrations constrains membership tightly while one that wandered constrains it loosely.

Definition at line 337 of file FeatureExtent.hpp.

{
    if (samples.empty())
        return {};
 
    const Eigen::Index n = samples.front().size();
    Eigen::VectorXd mean = Eigen::VectorXd::Zero(n);
    for (const auto& s : samples)
        mean += s;
    mean /= static_cast<double>(samples.size());
 
    Eigen::VectorXd var = Eigen::VectorXd::Zero(n);
    for (const auto& s : samples) {
        const Eigen::VectorXd d = s - mean;
        var += d.cwiseProduct(d);
    }
    var /= static_cast<double>(samples.size());
 
    Eigen::VectorXd radii(n);
    for (Eigen::Index i = 0; i < n; ++i)
        radii(i) = std::max(radius_sigma * std::sqrt(var(i)), 1e-9);
 
    return { .centre = mean, .radii = radii, .softness = softness };
}

References MayaFlux::mean().

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