Learning from complex real-life networks is a lively research area, with recent advances in learning information-rich, low-dimensional network node representations. However, state-of-the-art methods are not necessarily interpretable and are therefore not fully applicable to sensitive settings in biomedical or user profiling tasks, where explicit bias detection is highly relevant. The proposed SNoRe (Symbolic Node Representations) algorithm is capable of learning symbolic, human-understandable representations of individual network nodes, based on the similarity of neighborhood hashes which serve as features. SNoRe's interpretable features are suitable for direct explanation of individual predictions, which we demonstrate by coupling it with the widely used instance explanation tool SHAP to obtain nomograms representing the relevance of individual features for a given classification. To our knowledge, this is one of the first such attempts in a structural node embedding setting. In the experimental evaluation on eleven real-life datasets, SNoRe proved to be competitive to strong baselines, such as variational graph autoencoders, node2vec and LINE. The vectorized implementation of SNoRe scales to large networks, making it suitable for contemporary network learning and analysis tasks.
Nodes performing different functions in a network have different roles, and these roles can be gleaned from the structure of the network. Learning latent representations for the roles of nodes helps to understand the network and to transfer knowledge across networks. However, most existing structural embedding approaches suffer from high computation and space cost or rely on heuristic feature engineering. Here we propose RiWalk, a flexible paradigm for learning structural node representations. It decouples the structural embedding problem into a role identification procedure and a network embedding procedure. Through role identification, rooted kernels with structural dependencies kept are built to better integrate network embedding methods. To demonstrate the effectiveness of RiWalk, we develop two different role identification methods named RiWalk-SP and RiWalk-WL respectively and employ random walk based network embedding methods. Experiments on within-network classification tasks show that our proposed algorithms achieve comparable performance with other baselines while being an order of magnitude more efficient. Besides, we also conduct across-network role classification tasks. The results show potential of structural embeddings in transfer learning. RiWalk is also scalable, making it capable of capturing structural roles in massive networks.
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Deep Node Ranking (DNR) algorithm are competitive or better classification performance, significantly higher learning speed and lower space requirements when compared to state-of-the-art approaches on 15 real-life node classification benchmarks. Furthermore, it enables exploration of the relationship between symbolic and the derived sub-symbolic node representations, offering insights into the learned node space structure. To avoid the space complexity bottleneck in a direct node classification setting, DNR computes stationary distributions of personalized random walks from given nodes in mini-batches, scaling seamlessly to larger networks. The scaling laws associated with DNR were also investigated on 1488 synthetic Erd\H{o}s-R\'enyi networks, demonstrating its scalability to tens of millions of links.