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Network embedding has emerged as a promising research field for network analysis. Recently, an approach, named Barlow Twins, has been proposed for self-supervised learning in computer vision by applying the redundancy-reduction principle to the embedding vectors corresponding to two distorted versions of the image samples. Motivated by this, we propose Barlow Graph Auto-Encoder, a simple yet effective architecture for learning network embedding. It aims to maximize the similarity between the embedding vectors of immediate and larger neighborhoods of a node, while minimizing the redundancy between the components of these projections. In addition, we also present the variation counterpart named as Barlow Variational Graph Auto-Encoder. Our approach yields promising results for inductive link prediction and is also on par with state of the art for clustering and downstream node classification, as demonstrated by extensive comparisons with several well-known techniques on three benchmark citation datasets.

Heterogeneous Information Network (HIN) embedding refers to the low-dimensional projections of the HIN nodes that preserve the HIN structure and semantics. HIN embedding has emerged as a promising research field for network analysis as it enables downstream tasks such as clustering and node classification. In this work, we propose \ours for joint learning of cluster embeddings as well as cluster-aware HIN embedding. We assume that the connected nodes are highly likely to fall in the same cluster, and adopt a variational approach to preserve the information in the pairwise relations in a cluster-aware manner. In addition, we deploy contrastive modules to simultaneously utilize the information in multiple meta-paths, thereby alleviating the meta-path selection problem - a challenge faced by many of the famous HIN embedding approaches. The HIN embedding, thus learned, not only improves the clustering performance but also preserves pairwise proximity as well as the high-order HIN structure. We show the effectiveness of our approach by comparing it with many competitive baselines on three real-world datasets on clustering and downstream node classification.

In this paper, we study how to simultaneously learn two highly correlated tasks of graph analysis, i.e., community detection and node representation learning. We propose an efficient generative model called VECoDeR for jointly learning Variational Embeddings for Community Detection and node Representation. VECoDeR assumes that every node can be a member of one or more communities. The node embeddings are learned in such a way that connected nodes are not only "closer" to each other but also share similar community assignments. A joint learning framework leverages community-aware node embeddings for better community detection. We demonstrate on several graph datasets that VECoDeR effectively out-performs many competitive baselines on all three tasks i.e. node classification, overlapping community detection and non-overlapping community detection. We also show that VECoDeR is computationally efficient and has quite robust performance with varying hyperparameters.

In graph neural networks (GNNs), message passing iteratively aggregates nodes' information from their direct neighbors while neglecting the sequential nature of multi-hop node connections. Such sequential node connections e.g., metapaths, capture critical insights for downstream tasks. Concretely, in recommender systems (RSs), disregarding these insights leads to inadequate distillation of collaborative signals. In this paper, we employ collaborative subgraphs (CSGs) and metapaths to form metapath-aware subgraphs, which explicitly capture sequential semantics in graph structures. We propose meta\textbf{P}ath and \textbf{E}ntity-\textbf{A}ware \textbf{G}raph \textbf{N}eural \textbf{N}etwork (PEAGNN), which trains multilayer GNNs to perform metapath-aware information aggregation on such subgraphs. This aggregated information from different metapaths is then fused using attention mechanism. Finally, PEAGNN gives us the representations for node and subgraph, which can be used to train MLP for predicting score for target user-item pairs. To leverage the local structure of CSGs, we present entity-awareness that acts as a contrastive regularizer on node embedding. Moreover, PEAGNN can be combined with prominent layers such as GAT, GCN and GraphSage. Our empirical evaluation shows that our proposed technique outperforms competitive baselines on several datasets for recommendation tasks. Further analysis demonstrates that PEAGNN also learns meaningful metapath combinations from a given set of metapaths.

Variational autoencoder (VAE) is a widely used generative model for learning latent representations. Burda et al. in their seminal paper showed that learning capacity of VAE is limited by over-pruning. It is a phenomenon where a significant number of latent variables fail to capture any information about the input data and the corresponding hidden units become inactive. This adversely affects learning diverse and interpretable latent representations. As variational graph autoencoder (VGAE) extends VAE for graph-structured data, it inherits the over-pruning problem. In this paper, we adopt a model based approach and propose epitomic VGAE (EVGAE),a generative variational framework for graph datasets which successfully mitigates the over-pruning problem and also boosts the generative ability of VGAE. We consider EVGAE to consist of multiple sparse VGAE models, called epitomes, that are groups of latent variables sharing the latent space. This approach aids in increasing active units as epitomes compete to learn better representation of the graph data. We verify our claims via experiments on three benchmark datasets. Our experiments show that EVGAE has a better generative ability than VGAE. Moreover, EVGAE outperforms VGAE on link prediction task in citation networks.

We propose a new clustering algorithm, Extended Affinity Propagation, based on pairwise similarities. Extended Affinity Propagation is developed by modifying Affinity Propagation such that the desirable features of Affinity Propagation, e.g., exemplars, reasonable computational complexity and no need to specify number of clusters, are preserved while the shortcomings, e.g., the lack of global structure discovery, that limit the applicability of Affinity Propagation are overcome. Extended Affinity Propagation succeeds not only in achieving this goal but can also provide various additional insights into the internal structure of the individual clusters, e.g., refined confidence values, relative cluster densities and local cluster strength in different regions of a cluster, which are valuable for an analyst. We briefly discuss how these insights can help in easily tuning the hyperparameters. We also illustrate these desirable features and the performance of Extended Affinity Propagation on various synthetic and real world datasets., Comment: Submitted to TKDE