Abstract In this work, we explore multiplex graph (networks with different types of edges) generation with deep generative models. We discuss some of the challenges associated with multiplex graph generation that make it a more difficult problem than traditional graph generation. We propose TenGAN, the first neural network for multiplex graph generation, which greatly reduces the number of parameters required for multiplex graph generation. We also propose 3 different criteria for evaluating the quality of generated graphs: a graph-attribute-based, a classifier-based, and a tensor-based method. We evaluate its performance on 4 datasets and show that it generally performs better than other existing statistical multiplex graph generative models. We also adapt HGEN, an existing deep generative model for heterogeneous information networks, to work for multiplex graphs and show that our method generally performs better.

Abstract Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC decomposition (CPD), the ideal value for the number of components is known as the canonical rank and greatly affects the quality of the decomposition results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose FRAPPE , the first method to estimate the canonical rank of a tensor without having to compute the CPD. This method is the result of two key ideas. First, it is much cheaper to generate synthetic data with known rank compared to computing the CPD. Second, we can greatly improve the generalization ability and speed of our model by generating synthetic data that matches a given input tensor in terms of size and sparsity. We can then train a specialized single-use regression model on a synthetic set of tensors engineered to match a given input tensor and use that to estimate the canonical rank of the tensor—all without computing the expensive CPD. FRAPPE is over $$24\times $$ 24 × faster than the best-performing baseline, and exhibits a $$10\%$$ 10 % improvement in MAPE on a synthetic dataset. It also performs as well as or better than the baselines on real-world datasets.

Self-supervised learning on graphs has made large strides in achieving great performance in various downstream tasks. However, many state-of-the-art methods suffer from a number of impediments, which prevent them from realizing their full potential. For instance, contrastive methods typically require negative sampling, which is often computationally costly. While non-contrastive methods avoid this expensive step, most existing methods either rely on overly complex architectures or dataset-specific augmentations. In this paper, we ask: Can we borrow from classical unsupervised machine learning literature in order to overcome those obstacles? Guided by our key insight that the goal of distance-based clustering closely resembles that of contrastive learning: both attempt to pull representations of similar items together and dissimilar items apart. As a result, we propose CARL-G - a novel clustering-based framework for graph representation learning that uses a loss inspired by Cluster Validation Indices (CVIs), i.e., internal measures of cluster quality (no ground truth required). CARL-G is adaptable to different clustering methods and CVIs, and we show that with the right choice of clustering method and CVI, CARL-G outperforms node classification baselines on 4/5 datasets with up to a 79× training speedup compared to the best-performing baseline. CARL-G also performs at par or better than baselines in node clustering and similarity search tasks, training up to 1,500× faster than the best-performing baseline. Finally, we also provide theoretical foundations for the use of CVI-inspired losses in graph representation learning.

Graph generation is a task that has been explored with a wide variety of methods. Recently, several papers have applied Generative Adversarial Networks (GANs) to this task, but most of these methods result in graphs of full or unknown rank. Many real-world graphs have low rank, which roughly translates to the number of communities in that graph. Furthermore, it has been shown that taking the low rank approximation of a graph can defend against adversarial attacks. This suggests that testing models against graphs of different rank may be useful. However, current methods provide no way to control the rank of generated graphs. In this paper, we propose two variants of BRGAN: GAN architectures that generates synthetic graphs, which in addition to having realistic graph features, also have bounded rank. Our first variant, BRGAN-A, generates synthetic graphs competitive with state-of-the-art models, with rank equal to or lower than the desired rank. Our second variant, BRGAN-B, generates graphs of almost exactly the desired rank, but results in less realistic results. We also propose a novel rank penalty term on the generator, which allows us to control this realism-rank tradeoff.