Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis.

Conversely, GRevNets get the exact gradients at a minor additional cost, equivalent to one extra forward pass.

Network-wide Traffic State Estimation (TSE), which aims to infer a complete image of network traffic states with sparsely deployed sensors, plays a vital role in intelligent transportation systems. With the development of data-driven methods, traffic dynamics modeling has advanced significantly. However, TSE poses fundamental challenges for data-driven approaches, since historical patterns cannot be learned locally at sensor-free segments. Although inductive graph learning shows promise in estimating states at locations without sensor, existing methods typically handle unobserved locations by filling them with zeros, introducing bias to the sensitive graph message propagation. The recently proposed Dirichlet Energy-based Feature Propagation (DEFP) method achieves State-Of-The-Art (SOTA) performance in unobserved node classification by eliminating the need for zero-filling. However, applying it to TSE faces three key challenges: inability to handle directed traffic networks, strong assumptions in traffic spatial correlation modeling, and overlooks distinct propagation rules of different patterns (e.g., congestion and free flow). We propose DGAE, a novel inductive graph representation model that addresses these challenges through theoretically derived DEFP for Directed graph (DEFP4D), enhanced spatial representation learning via DEFP4D-guided latent space encoding, and physics-guided propagation mechanisms that separately handles congested and free-flow patterns. Experiments on three traffic datasets demonstrate that DGAE outperforms existing SOTA methods and exhibits strong cross-city transferability. Furthermore, DEFP4D can serve as a standalone lightweight solution, showing superior performance under extremely sparse sensor conditions.

We propose a method to represent bipartite networks using graph embeddings tailored to tackle the challenges of studying ecological networks, such as the ones linking plants and pollinators, where many covariates need to be accounted for, in particular to control for sampling bias. We adapt the variational graph auto-encoder approach to the bipartite case, which enables us to generate embeddings in a latent space where the two sets of nodes are positioned based on their probability of connection. We translate the fairness framework commonly considered in sociology in order to address sampling bias in ecology. By incorporating the Hilbert-Schmidt independence criterion (HSIC) as an additional penalty term in the loss we optimize, we ensure that the structure of the latent space is independent of continuous variables, which are related to the sampling process. Finally, we show how our approach can change our understanding of ecological networks when applied to the Spipoll data set, a citizen science monitoring program of plant-pollinator interactions to which many observers contribute, making it prone to sampling bias.

The (variational) graph auto-encoder is extensively employed for learning representations of graph-structured data. However, the formation of real-world graphs is a complex and heterogeneous process influenced by latent factors. Existing encoders are fundamentally holistic, neglecting the entanglement of latent factors. This not only makes graph analysis tasks less effective but also makes it harder to understand and explain the representations. Learning disentangled graph representations with (variational) graph auto-encoder poses significant challenges, and remains largely unexplored in the existing literature. In this article, we introduce the Disentangled Graph Auto-Encoder (DGA) and Disentangled Variational Graph Auto-Encoder (DVGA), approaches that leverage generative models to learn disentangled representations. Specifically, we first design a disentangled graph convolutional network with multi-channel message-passing layers, as the encoder aggregating information related to each disentangled latent factor. Subsequently, a component-wise flow is applied to each channel to enhance the expressive capabilities of disentangled variational graph auto-encoder. Additionally, we design a factor-wise decoder, considering the characteristics of disentangled representations. In order to further enhance the independence among representations, we introduce independence constraints on mapping channels for different latent factors. Empirical experiments on both synthetic and real-world datasets show the superiority of our proposed method compared to several state-of-the-art baselines.

Graph auto-encoders are widely used to construct graph representations in Euclidean vector spaces. However, it has already been pointed out empirically that linear models on many tasks can outperform graph auto-encoders. In our work, we prove that the solution space induced by graph auto-encoders is a subset of the solution space of a linear map. This demonstrates that linear embedding models have at least the representational power of graph auto-encoders based on graph convolutional networks. So why are we still using nonlinear graph auto-encoders? One reason could be that actively restricting the linear solution space might introduce an inductive bias that helps improve learning and generalization. While many researchers believe that the nonlinearity of the encoder is the critical ingredient towards this end, we instead identify the node features of the graph as a more powerful inductive bias. We give theoretical insights by introducing a corresponding bias in a linear model and analyzing the change in the solution space. Our experiments are aligned with other empirical work on this question and show that the linear encoder can outperform the nonlinear encoder when using feature information.

With the explosion of graph-structured data, link prediction has emerged as an increasingly important task. Embedding methods for link prediction utilize neural networks to generate node embeddings, which are subsequently employed to predict links between nodes. However, the existing embedding methods typically take a holistic strategy to learn node embeddings and ignore the entanglement of latent factors. As a result, entangled embeddings fail to effectively capture the underlying information and are vulnerable to irrelevant information, leading to unconvincing and uninterpretable link prediction results. To address these challenges, this paper proposes a novel framework with two variants, the disentangled graph auto-encoder (DGAE) and the variational disentangled graph auto-encoder (VDGAE). Our work provides a pioneering effort to apply the disentanglement strategy to link prediction. The proposed framework infers the latent factors that cause edges in the graph and disentangles the representation into multiple channels corresponding to unique latent factors, which contributes to improving the performance of link prediction. To further encourage the embeddings to capture mutually exclusive latent factors, we introduce mutual information regularization to enhance the independence among different channels. Extensive experiments on various real-world benchmarks demonstrate that our proposed methods achieve state-of-the-art results compared to a variety of strong baselines on link prediction tasks. Qualitative analysis on the synthetic dataset also illustrates that the proposed methods can capture distinct latent factors that cause links, providing empirical evidence that our models are able to explain the results of link prediction to some extent. All code will be made publicly available upon publication of the paper.

The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph structure by only considering two nodes at a time, thus ignoring possible interactions among edges. On the other hand, structured prediction, which considers the whole graph simultaneously, is computationally expensive. In this paper, we utilize the well-known triadic closure property which is exhibited in many real-world networks. We propose the triad decoder, which considers and predicts the three edges involved in a local triad together. The triad decoder can be readily used in any graph-based auto-encoder. In particular, we incorporate this to the (variational) graph auto-encoder. Experiments on link prediction, node clustering and graph generation show that the use of triads leads to more accurate prediction, clustering and better preservation of the graph characteristics.

Reconstructing components of a genomic mixture from data obtained by means of DNA sequencing is a challenging problem encountered in a variety of applications including single individual haplotyping and studies of viral communities. High-throughput DNA sequencing platforms oversample mixture components to provide massive amounts of reads whose relative positions can be determined by mapping the reads to a known reference genome; assembly of the components, however, requires discovery of the reads' origin -- an NP-hard problem that the existing methods struggle to solve with the required level of accuracy. In this paper, we present a learning framework based on a graph auto-encoder designed to exploit structural properties of sequencing data. The algorithm is a neural network which essentially trains to ignore sequencing errors and infers the posteriori probabilities of the origin of sequencing reads. Mixture components are then reconstructed by finding consensus of the reads determined to originate from the same genomic component. Results on realistic synthetic as well as experimental data demonstrate that the proposed framework reliably assembles haplotypes and reconstructs viral communities, often significantly outperforming state-of-the-art techniques.

We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. This decoupling enables the independent and fixed design of the auto-encoder without requiring additional GCN layers for every desired increase in the size of a node's local receptive field. Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field in building representations. Furthermore a by-product of fixing the auto-encoder design often results in substantially smaller networks than their VGAE counterparts especially as we increase the number of feature propagations. A comparative downstream evaluation on link prediction tasks show comparable state of the art performance to similar VGAE arrangements despite considerable simplification. We also show the simple application of our methodology to more challenging representation learning scenarios such as spatio-temporal graph representation learning.