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.
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