# GraphGAN: Graph Representation Learning with Generative Adversarial Nets

national conference on artificial intelligence, 2018.

EI

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Wei bo:

Abstract:

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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Summary

- 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.

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