adapt.metrics.frechet_distance

adapt.metrics.frechet_distance(Xs, Xt)

Compute the frechet distance between Xs and Xt.

\[\Delta = ||\mu_S - \mu_T||_2^2 + Tr\left(\Sigma_S + \Sigma_T - 2 (\Sigma_S \cdot \Sigma_T)^{\frac{1}{2}} \right)\]

Where:

• \(\mu_S, \mu_T\) are the mean of Xs, Xt along first axis.

• \(\Sigma_S, \Sigma_T\) are the covariance matrix of Xs, Xt.

Parameters

Xsarray

Source array

Xtarray

Target array

Returns

scorefloat

See also

normalized_frechet_distance

linear_discrepancy

normalized_linear_discrepancy

References

1

[1] Dowson, D. C; Landau, B. V. “The Fréchet distance between multivariate normal distributions”. JMVA. 1982