GraphGAN: Graph Representation Learning with Generative Adversarial Nets
national conference on artificial intelligence, 2018.
link predictionreal worlddiscriminative modellow dimensional vectornetwork analysisMore(11+)
Under the GraphGAN framework, both the generator and the discriminator could benefit from each other: the generator is guided by the signals from the discriminator and improves its generating performance, while the discriminator is pushed by the generator to better distinguish gr...
The goal of graph representation learning is to embed each vertex in a graph into a low-dimensional vector space. Existing graph representation learning methods can be classified into two categories: generative models that learn the underlying connectivity distribution in the graph, and discriminative models that predict the probability o...More
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- Known as network embedding, aims to represent each vertex in a graph as a low-dimensional vector, which could facilitate tasks of network analysis and prediction over vertices and edges.
- We aim to train two models during the learning process of GraphGAN: 1) Generator G(v|vc), which tries to fit the underlying true connectivity distribution ptrue(v|vc) as much as possible, and generates the most likely vertices to be connected with vc; 2) Discriminator D(v, vc), which tries to distinguish well-connected vertex pairs from ill-connected ones, and calculates the probability of whether an edge exists between v and vc.
- Given the graph G, we aim to learn the following two models: Generator G(v|vc; θG), which tries to approximate the underlying true connectivity distribution ptrue(v|vc), and generates the most likely vertices to be connected with vc from vertex set V.
- The calculation of softmax in Eq (5) involves all vertices in the graph, which implies that for each generated sample v, we need to calculate gradients ∇θG log G(v|vc; θG) and update all vertices.
- The key idea of graph softmax is to define a new method of computing connectivity distribution in generator G(·|vc; θG) that satisfies the following three desirable properties:
- The maximal length of the path is log V , which is the depth of the BFS-tree, and each vertex in the path is connected to d vertices on average.
- For a given vertex pair, we aim to reveal how the probability of edge existence changes with their shortest distance in the graph.
- The above finding empirically demonstrates that the probability of edge existence between a pair of vertices is approximately exponentially proportional to the inverse of their shortest distance, which strongly proves that graph softmax captures the essence of real-world graphs according to Theorem 2.
- We obtain the representation vectors for all vertices and use logistic regression method to predict the probability of edge existence for a given vertex pair.
- The result suggests that, different with IRGAN (Wang et al 2017a), the design of graph softmax enables the generator in GraphGAN to draw samples and learn vertex embeddings more efficiently.
- We train GraphGAN and baselines on the whole graph to obtain vertex representations, and use logistic regression as classifier to perform node classification with 9:1 train-test ratio.
- We propose GraphGAN that unifies two schools of graph representation learning methodologies, i.e., generative methods and discriminative methods, via adversarial training in a minimax game.
- We conduct experiments on five real-world datasets in three scenarios, and the results demonstrate that GraphGAN significantly outperforms strong baselines in all experiments due to its adversarial framework and proximity-aware graph softmax.