text: Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an unsupervised learning task by explicitly preserving the structural connectivity in the network, or (2) whether the embedding is a by-product during the supervised learning of a specific discriminative task in a deep neural network. In this paper, we focus on bridging the gap of the two lines of the research. We propose to adapt the Generative Adversarial model to perform network embedding, in which the generator is trying to generate vertex pairs, while the discriminator tries to distinguish the generated vertex pairs from real connections (edges) in the network. Wasserstein-1 distance is adopted to train the generator to gain better stability. We develop three variations of models, including GANE which applies cosine similarity, GANE-O1 which preserves the first-order proximity, and GANE-O2 which tries to preserves the second-order proximity of the network in the low-dimensional embedded vector space. We later prove that GANE-O2 has the same objective function as GANE-O1 when negative sampling is applied to simplify the training process in GANE-O2. Experiments with real-world network datasets demonstrate that our models constantly outperform state-of-the-art solutions with significant improvements on precision in link prediction, as well as on visualizations and accuracy in clustering tasks.
  @cite_15: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
summary: Recent advances in Generative Adversarial Networks (GANs) @cite_15 have proven GANs as a powerful framework for learning complex data distributions. The core idea is to define the generator and the discriminator to be the minimax game players competing with each other to push the generator to produce high quality data to fool the discriminator.