Fig. 6.

For each pair of hyperparameters $p$ and $k$ of the proposed unsupervised algorithm the hyperparameters of the top layer ($n$, $m$, $\beta$) were optimized on the validation set. For these optimal ($n$, $m$, $\beta$), the mean error together with the SD of the individual runs on the held-out test set is shown for each pair of Lebesgue norm $p$ and the ranking parameter $k$. In these experiments the hyperparameter $\mathrm{\Delta }$ was set to the optimal value $\mathrm{\Delta }=0.4$ determined on the validation set. The unsupervised algorithm did not converge for ($p=2$, $k=8$) and ($p=6$, $k=8$), indicating that a smaller value of $\mathrm{\Delta }$ is required for those hyperparameters.