边替换文法：一种生成图的形式语言方法
Edge Replacement Grammars: A Formal Language Approach for Generating Graphs
摘要：
图作为结构化数据的模型越来越普遍。一个生成模型，密切模仿一组给定的图的结构特性，在各种领域的效用。许多现有的工作需要大量的参数，实际上是指数的大小的图形，从数据中估计。我们采取稍微不同的方法来解决这个问题，利用广泛的正式的图形语法文献的工作。在本文中，我们提出了一个基于概率边替换文法（PERG）的图生成模型。我们提出了一个变种的PERG称为限制PERG（RPERG），这是类似于PCFG在字符串语法文献。有了这个限制，我们就能够推导出一个学习算法，用于从图形数据中估计文法的参数。我们经验证明，在现实生活中的数据集，RPERG优于现有的图形生成方法。我们改进了最先进的基于超边替换语法的图生成模型的性能。尽管是一个上下文无关文法，该模型是能够捕捉到许多真实网络的结构特性，如度分布，幂律和谱特性。
英文摘要：
Graphs are increasingly becoming ubiquitous as models for structured data. A generative model that closely mimics the structural properties of a given set of graphs has utility in a variety of domains. Much of the existing work require that a large number of parameters, in fact exponential in size of the graphs, be estimated from the data. We take a slightly different approach to this problem, leveraging the extensive prior work in the formal graph grammar literature. In this paper, we propose a graph generation model based on Probabilistic Edge Replacement Grammars (PERGs). We propose a variant of PERG called Restricted PERG (RPERG), which is analogous to PCFGs in string grammar literature. With this restriction, we are able to derive a learning algorithm for estimating the parameters of the grammar from graph data. We empirically demonstrate on real life datasets that RPERGs outperform existing methods for graph generation. We improve on the performance of the state-of-the-art Hyperedge Replacement Grammar based graph generative model. Despite being a context free grammar, the proposed model is able to capture many of the structural properties of real networks, such as degree distributions, power law and spectral characteristics.
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