  We construct new, multivariate empirical relations for measuring neutron star
radii and tidal deformabilities from the dominant gravitational wave frequency
in the post-merger phase of binary neutron star mergers. The relations
determine neutron star radii and tidal deformabilities for specific neutron
star masses with consistent accuracy and depend only on two observables: the
post-merger peak frequency $f_{\rm peak}$ and the chirp mass $M_{\rm chirp}$.
The former could be measured with good accuracy from gravitational waves
emitted in the post-merger phase using next-generation detectors, whereas the
latter is already obtained with good accuracy from the inspiral phase with
present-day detectors. Our main data set consists of a gravitational wave
catalogue obtained with CFC/SPH simulations. We also extract the $f_{\rm peak}$
frequency from the publicly available CoRe data set, obtained through
grid-based GRHD simulations and find good agreement between the extracted
frequencies of the two data sets. As a result, we can construct empirical
relations for the combined data sets. Furthermore, we investigate empirical
relations for two secondary peaks, $f_{2-0}$ and $f_{\rm spiral}$, and show
that these relations are distinct in the whole parameter space, in agreement
with a previously introduced spectral classification scheme. Finally, we show
that the spectral classification scheme can be reproduced using
machine-learning techniques.
