Evaluating Loss Functions for Graph Neural Networks: Towards Pretraining and Generalization

Graph Neural Networks (GNNs) became useful for learning on non-Euclidean data. However, their best performance depends on choosing the right model architecture and the training objective, also called the loss function. Researchers have studied these parts separately, but a large-scale evaluation has not looked at how GNN models and many loss functions work together across different tasks. To fix this, we ran a thorough study - it included seven well-known GNN architectures. We also used a large group of 30 single plus mixed loss functions. The study looked at both inductive and transductive settings. Our evaluation spanned three distinct real-world datasets, assessing performance in both inductive and transductive settings using 21 comprehensive evaluation metrics. From these extensive results (detailed in supplementary information 1 \& 2), we meticulously analyzed the top ten model-loss combinations for each metric based on their average rank. Our findings reveal that, especially for the inductive case: 1) Hybrid loss functions generally yield superior and more robust performance compared to single loss functions, indicating the benefit of multi-objective optimization. 2) The GIN architecture always showed the highest-level average performance, especially with Cross-Entropy loss. 3) Although some combinations had overall lower average ranks, models such as GAT, particularly with certain hybrid losses, demonstrated incredible specialized strengths, maximizing the most top-1 results among the individual metrics, emphasizing subtle strengths for particular task demands. 4) On the other hand, the MPNN architecture typically lagged behind the scenarios it was tested against.

TempNodeEmb:Temporal Node Embedding considering temporal edge influence matrix

Understanding the evolutionary patterns of real-world evolving complex systems such as human interactions, transport networks, biological interactions, and computer networks has important implications in our daily lives. Predicting future links among the nodes in such networks reveals an important aspect of the evolution of temporal networks. To analyse networks, they are mapped to adjacency matrices, however, a single adjacency matrix cannot represent complex relationships (e.g. temporal pattern), and therefore, some approaches consider a simplified representation of temporal networks but in high-dimensional and generally sparse matrices. As a result, adjacency matrices cannot be directly used by machine learning models for making network or node level predictions. To overcome this problem, automated frameworks are proposed for learning low-dimensional vectors for nodes or edges, as state-of-the-art techniques in predicting temporal patterns in networks such as link prediction. However, these models fail to consider temporal dimensions of the networks. This gap motivated us to propose in this research a new node embedding technique which exploits the evolving nature of the networks considering a simple three-layer graph neural network at each time step, and extracting node orientation by Given's angle method. To prove our proposed algorithm's efficiency, we evaluated the efficiency of our proposed algorithm against six state-of-the-art benchmark network embedding models, on four real temporal networks data, and the results show our model outperforms other methods in predicting future links in temporal networks.