Fréchet distance

Summary

Fréchet distance is a measure of similarity between two curves or point clouds. It was used by (1) to measure the similarity of designed proteins.

$$\text{FPD}=\Vert {\mu }_{\text{test}}-{\mu }_{\text{gen}}{\Vert }^2+\mathrm{Tr}\left(C_{\text{test}}+C_{\text{gen}}-2\sqrt{C_{\text{test}}{C}_{\text{gen}}}\right)$$

$\mu$: Mean of set $C$: Covariance matrix $Tr$: Trace (sum of components along diagonal)

1.

Alamdari S, Thakkar N, van den Berg R, Tenenholtz N, Strome R, Moses AM, et al. Protein generation with evolutionary diffusion: sequence is all you need. openRxiv; 2023. Available from: https://doi.org/10.1101/2023.09.11.556673