# Edge Convolutional Networks for Style Change Detection in Arabic Multi-Authored Text
## 4 Proposed Solution: ECNN-ASCD
### GNNs for the SCD Task  
The graph edges proposed in Section 4.2 represent the writing styles. These styles need to be classified for the SCD task. Thus, EdgeConv was adapted to handle the edge representations. Figure 3 shows the ECNN-ASCD's architecture. The input graph \(\mathcal{G}^{(0)}\) has initial node representations \(X_{N\times F^{(0)}}^{(0)}\) with an empty set of edge representations, where \(N\times F^{(0)}\) represents the shape of the node representation matrix. To extract more non-local features, the ECNN-ASCD's architecture comprises four layers. They contain the same components except the first layer. Every layer \(k\) generates new edge representations \(E_{N-1\times F^{(k)}}^{(k)}\), where the number of edges is equal to the number of nodes minus one. Every layer's node and edge representations are input to the subsequent layer. The symbol \(\oplus\) indicates to sum the required information to obtain the edge representations. After passing through four layers, the output graph \(\mathcal{G}^{(4)}\) is obtained with node representations \(X_{N\times F^{(k)}}^{(4)}\) and edge representations \(E_{N-1\times F^{(4)}}^{(4)}\). The ECNN-ASCD's architecture ends with a single FC layer. It classifies the edge representations extracted from the last layer. Moreover, activation functions introduce non-linearities in mapping input values to desired outputs during training instead of being restricted to modeling only linear relationships. Two activation functions were adopted: ReLU and Sigmoid. ReLU has a simple mathematical operation, the comparison to zero, which helps get faster training times in deep networks. Sigmoid is placed at the final layer before detecting using a threshold of 0.5 to round outputs to 0 and 1. Figure 3: ECNN-ASCD architecture, where the colors are utilized for component separation. Figure 2: Example of a graph design: (**a**) a path graph used in ECNN-ASCD; (**b**) a complete graph. The default EdgeConv module feeds the input node representations into a neural network. In ECNN-ASCD, two sequential linear layers are used as the neural network. The first layer concatenates node representations with those of their neighbors. This concatenation results in a doubling of the input size. The second layer maps the concatenated node representations to half of their size. Thus, the EdgeConv module reduces the input size. Therefore, FC layers are inserted in every ECNN-ASCD layer to apply a linear transformation to the representation vectors. The aggregation method in this EdgeConv module calculates the mean value of the transformed neighbor representations to update the target node representations. Algorithm 3 outlines the operations performed in every ECNN-ASCD layer. A layer \(k\) receives the graph resulting from the previous layer \(\mathcal{G}^{(k-1)}\). Their edge representations \(E^{(k-1)}\) are extracted, whereas the first layer does not receive the previous edge representations because they have an empty set. The previous node representations, \(X^{(k-1)}\), are fed into the EdgeConv module to generate the new node representations, \(X^{(k)}\). The initial node representations, \(X^{(0)}\), are added in each GNN layer to alleviate the over-smoothing issue. These representations are aggregated by summing them. Thus, the edge representations in the layer \(k\) are updated and adjusted across layers.