A Survey on Embedding Dynamic Graphs

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks present dynamic behavior, including topological evolution, feature evolution, and diffusion. Therefore, several methods for embedding dynamic graphs have been proposed to learn network representations over time, facing novel challenges, such as time-domain modeling, temporal features to be captured, and the temporal granularity to be embedded. In this survey, we overview dynamic graph embedding, discussing its fundamentals and the recent advances developed so far. We introduce the formal definition of dynamic graph embedding, focusing on the problem setting and introducing a novel taxonomy for dynamic graph embedding input and output. We further explore different dynamic behaviors that may be encompassed by embeddings, classifying by topological evolution, feature evolution, and processes on networks. Afterward, we describe existing techniques and propose a taxonomy for dynamic graph embedding techniques based on algorithmic approaches, from matrix and tensor factorization to deep learning, random walks, and temporal point processes. We also elucidate main applications, including dynamic link prediction, anomaly detection, and diffusion prediction, and we further state some promising research directions in the area.

Formal Links between Feature Diversity and Phylogenetic Diversity

The extent to which phylogenetic diversity (PD) captures feature diversity (FD) is a topical and controversial question in biodiversity conservation. In this short paper, we formalize this question and establish a precise mathematical condition for FD (based on discrete characters) to coincide with PD. In this way, we make explicit the two main reasons why the two diversity measures might disagree for given data; namely, the presence of certain patterns of feature evolution and loss, and using temporal branch lengths for PD in settings that may not be appropriate (e.g., due to rapid evolution of certain features over short periods of time). Our article also explores the relationship between the “Fair Proportion” index of PD and a simple index of FD (both of which correspond to Shapley values in cooperative game theory). In a second mathematical result, we show that the two indices can take identical values for any phylogenetic tree, provided the branch lengths in the tree are chosen appropriately. [Evolutionary distinctiveness; feature diversity; phylogenetic diversity; shapley value.]

Formal Links between Feature Diversity and Phylogenetic Diversity

The extent to which phylogenetic diversity (PD) captures feature diversity (FD) is a topical and controversial question in biodiversity conservation. In this short paper, we formalise this question and establish a precise mathematical condition for FD (based on discrete characters) to coincide with PD. In this way, we make explicit the two main reasons why the two diversity measures might disagree for given data; namely, the presence of certain patterns of feature evolution and loss, and using temporal branch lengths for PD in settings that may not be appropriate (e.g. due to rapid evolution of certain features over short periods of time). Our paper also explores the relationship between the ‘Fair Proportion’ index of PD and a simple index of FD (both of which correspond to Shapley values in cooperative game theory). In a second mathematical result, we show that the two indices can take identical values for any phylogenetic tree, provided the branch lengths in the tree are chosen appropriately.

Feature Evolution Based Multi-Task Learning for Collaborative Filtering with Social Trust

Social recommendation could address the data sparsity and cold-start problems for collaborative filtering by leveraging user trust relationships as auxiliary information for recommendation. However, most existing methods tend to consider the trust relationship as preference similarity in a static way and model the representations for user preference and social trust via a common feature space. In this paper, we propose TrustEV and take the view of multi-task learning to unite collaborative filtering for recommendation and network embedding for user trust. We design a special feature evolution unit that enables the embedding vectors for two tasks to exchange their features in a probabilistic manner, and further harness a meta-controller to globally explore proper settings for the feature evolution units. The training process contains two nested loops, where in the outer loop, we optimize the meta-controller by Bayesian optimization, and in the inner loop, we train the feedforward model with given feature evolution units. Experiment results show that TrustEV could make better use of social information and greatly improve recommendation MAE over state-of-the-art approaches.