Main paper can be found here.

Constructs GCN which is node and edge type aware, called R-GCN
Mainly useful for relational multi-graphs
Demonstrate its effectiveness over entity classification and link prediction tasks

R-GCN layer is defined with the following equation
$$ h_i^{l+1} = \sigma( \Sigma_{r \in R} \Sigma_{j \in N_i^r} \frac{1}{c_{i,r}} W_r^l h_j^l + W_0^l h_i^l)$$
where:
- $$R$$ = set of all relations
- $$l$$ = l-th layer in the R-GCN model
- $$h_i$$ = hidden embeddings of i-th node
- $$\sigma$$ = activation function
- $$N_i^r$$ = neighborhood of i-th node on relation type r
- $$c_{i,r}$$ = normalization value which can be learnt are a constant (eg: $$|N_i^r|$$)
- $$W_r^l$$ = weights for the l-th layer on relation type r
- $$W_0^l$$ = weights for the l-th layer on self-loop
basis decomposition based regularization
- $$W_r^l = \Sigma_{b \in [0,B)} a_{rb}^l V_b^l$$
- $$a_{rb}^l$$ = coefficients to be learnt
- $$V_b^l$$ = basis matrices to be learnt
- $$B$$ = number of bases
block-diagonal based regularization
- $$W_r^l = diag_{b \in [0,B)} Q_{br}^l$$
- $$Q_{br}^l$$ = matrices to be learnt of dimension $$\frac{d^{l+1}}{B} \times \frac{d^{l}}{B}$$
- $$d^l$$ = embedding dimension of l-th layer