论文标题
单条件地图方程
Single-trajectory map equation
论文作者
论文摘要
社区检测，在网络上代表的复杂系统中识别模块结构的过程是各个科学领域的有效工具。地图方程是一种基于网络上随机步行的信息理论框架，是一种特别受欢迎的社区检测方法。尽管在许多应用中表现出色，但尚未对地图方程式的内部工作进行彻底研究。在此，我们重新访问了地图方程的原始公式，并解决了其``原始形式''的存在，我们称为单个点标地图方程。这种原始形式阐明了地图方程原理背后的许多细节，这些原理隐藏在随机步行的稳态极限中。最重要的是，单条件图方程提供了更加平衡的社区结构，自然降低了地图方程中过度拟合现象的趋势。
Community detection, the process of identifying module structures in complex systems represented on networks, is an effective tool in various fields of science. The map equation, which is an information-theoretic framework based on the random walk on a network, is a particularly popular community detection method. Despite its outstanding performance in many applications, the inner workings of the map equation have not been thoroughly studied. Herein, we revisit the original formulation of the map equation and address the existence of its ``raw form,'' which we refer to as the single-trajectory map equation. This raw form sheds light on many details behind the principle of the map equation that are hidden in the steady-state limit of the random walk. Most importantly, the single-trajectory map equation provides a more balanced community structure, naturally reducing the tendency of the overfitting phenomenon in the map equation.
