DINE: Dimensional Interpretability of Node Embeddings

Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a latent vector space, allowing their use for various graph tasks. Despite their success, only few studies have focused on explaining node embeddings locally. Moreover, global explanations of node embeddings remain unexplored, limiting interpretability and debugging potentials. We address this gap by developing human-understandable explanations for dimensions in node embeddings. Towards that, we first develop new metrics that measure the global interpretability of embedding vectors based on the marginal contribution of the embedding dimensions to predicting graph structure. We say that an embedding dimension is more interpretable if it can faithfully map to an understandable sub-structure in the input graph - like community structure. Having observed that standard node embeddings have low interpretability, we then introduce DINE (Dimension-based Interpretable Node Embedding), a novel approach that can retrofit existing node embeddings by making them more interpretable without sacrificing their task performance. We conduct extensive experiments on synthetic and real-world graphs and show that we can simultaneously learn highly interpretable node embeddings with effective performance in link prediction.

Time-varying Graph Representation Learning via Higher-Order Skip-Gram with Negative Sampling

Representation learning models for graphs are a successful family of techniques that project nodes into feature spaces that can be exploited by other machine learning algorithms. Since many real-world networks are inherently dynamic, with interactions among nodes changing over time, these techniques can be defined both for static and for time-varying graphs. Here, we build upon the fact that the skip-gram embedding approach implicitly performs a matrix factorization, and we extend it to perform implicit tensor factorization on different tensor representations of time-varying graphs. We show that higher-order skip-gram with negative sampling (HOSGNS) is able to disentangle the role of nodes and time, with a small fraction of the number of parameters needed by other approaches. We empirically evaluate our approach using time-resolved face-to-face proximity data, showing that the learned time-varying graph representations outperform state-of-the-art methods when used to solve downstream tasks such as network reconstruction, and to predict the outcome of dynamical processes such as disease spreading. The source code and data are publicly available at https://github.com/simonepiaggesi/hosgns.