Over the past years, Generative Adversarial Networks (GANs) have shown a remarkable generation performance especially in image synthesis. Unfortunately, they are also known for having an unstable training process and might loose parts of the data distribution for heterogeneous input data. In this paper, we propose a novel GAN extension for multi-modal distribution learning (MMGAN). In our approach, we model the latent space as a Gaussian mixture model with a number of clusters referring to the number of disconnected data manifolds in the observation space, and include a clustering network, which relates each data manifold to one Gaussian cluster. Thus, the training gets more stable. Moreover, MMGAN allows for clustering real data according to the learned data manifold in the latent space. By a series of benchmark experiments, we illustrate that MMGAN outperforms competitive state-of-the-art models in terms of clustering performance.

Classical stochastic models, such as the Erd os-R enyi, Barabasi-Albert, and the stochastic block model generate graphs based on a predefined set of parameters, such as the probability of edge formation within and between communities [1]. In contrast, modern approaches to graph generation based on deep learning, including NetGAN [2], GraphGAN [3], and GraphRNN [4], are flexible enough to learn multiple different properties of an input graph simultaneously. The graphs generated by these architectures may be used for downstream learning tasks such as data augmentation [5], recommendation [6], and link prediction [7]. Many real-world networks consist of entities with complex mutual interrelations. Such networks cannot be modeled effectively as graphs with simple pairwise relations, despite the fact that pairwise relations provide a wealth of information for learning. Studying higher-order relationships in a graph is fundamental for our understanding of the network behavior and function. Higher-order relationships are usually termed hyperedges (collections of more than two nodes) [8, 9] or network motifs (recurrent node connectivity patterns that are statistically significant compared to some ground truth random graph model) [10]. These higher-order structures are the actual building blocks of complex networks, as they capture fundamental functional properties.