揭示node2vec随机游走的稳定分布，可调控生成不同分布类型。
Stationary distribution of node2vec random walks on household models
- 基于家庭模型图，推导node2vec稳定分布的显式表达式。
- 调节参数可实现均匀、大小偏向或简单随机游走的分布形态。
- 为网络嵌入中的游走策略设计提供理论依据，适合图学习研究者。
node2vec随机游走在网络嵌入算法中已被证明是关键工具。这类游走具有可调性，其转移概率依赖于前一访问节点以及当前与前一节点共同构成的三角形。尽管该方法在实践中广泛应用，但node2vec游走的大多数数学性质仍缺乏深入研究，尤其是其平稳分布。本文研究了在社区结构的家庭模型图上的node2vec随机游走，证明了其平稳分布可由游走参数显式描述。通过调节参数，平稳分布可在均匀分布、大小偏向分布或简单随机游走分布之间插值，展示了可能游走的广泛范围。此外，还在一些具体图设置下进一步探索了这些效应。
原文摘要 · Abstract (English)
The node2vec random walk has proven to be a key tool in network embedding algorithms. These random walks are tuneable, and their transition probabilities depend on the previous visited node and on the triangles containing the current and the previously visited node. Even though these walks are widely used in practice, most mathematical properties of node2vec walks are largely unexplored, including their stationary distribution. We study the node2vec random walk on community-structured household model graphs. We prove an explicit description of the stationary distribution of node2vec walks in terms of the walk parameters. We then show that by tuning the walk parameters, the stationary distribution can interpolate between uniform, size-biased, or the simple random walk stationary distributions, demonstrating the wide range of possible walks. We further explore these effects on some specific graph settings.
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