{y}{h}({e})]_+ \,,\end{aligned}$$ with $[\cdot]_+$ the positive part of the argument. Alternatively, one can opt to optimize a probabilistic loss function like the logistic loss: $$\begin{aligned}
{\mathcal{L}}({h}({e}),{y}) = \ln(1+\exp(-{y}{h}({e}))) \,.\end{aligned}$$ Conversely, if in a given application the observed relations are graded instead of crisp, other loss functions have to be considered. Hence, we will run experiments with a least-squares loss function: $$\label{regrloss}
{\mathcal{L}}({h}({e}),{y}) = ({y}_{e}-{h}({e}))^2 \,,$$ resulting in a regression type of learning setting. Alternatively, one could prefer to optimize a more robust regression loss like the $\epsilon$-insensitive loss, in case outliers are expected in the training dataset. So far, our framework does not differ from standard classification and regression algorithms. However, the specification of a more precise model structure for (\[eq:primalmodel\]) offers a couple of new challenges. In the most general case, when no further restrictions on the underlying relation can be specified, the following Kronecker product feature mapping is proposed to express pairwise interactions between features of nodes: $$\begin{aligned}
\Phi({e}) = \Phi({v},{v}') = \phi({v}) \otimes \phi({v}')\,,\end{aligned}$$ where $\phi$ represents the feature mapping for individual nodes. A formal definition of the Kronecker product can be found in the appendix. As first shown in [@Ben-Hur2005], the Kronecker product pairwise feature mapping 