Complex systems, represented as dynamic networks, comprise of components that influence each other via direct and/or indirect interactions. Recent research has shown the importance of using Higher-Order Networks (HONs) for modeling and analyzing such complex systems, as the typical Markovian assumption in developing the First Order Network (FON) can be limiting. This higher-order network representation not only creates a more accurate representation of the underlying complex system, but also leads to more accurate network analysis. In this paper, we first present a scalable and accurate model, BuildHON+, for higher-order network representation of data derived from a complex system with various orders of dependencies. Then, we show that this higher-order network representation modeled by BuildHON+ is significantly more accurate in identifying anomalies than FON, demonstrating a need for the higher-order network representation and modeling of complex systems for deriving meaningful conclusions.

中文翻译：

---

网络中高阶依存关系的高效建模：从算法到异常检测的应用

表示为动态网络的复杂系统由通过直接和/或间接交互而相互影响的组件组成。最近的研究表明，使用高阶网络（HON）来建模和分析此类复杂系统非常重要，因为开发一阶网络（FON）时通常采用的马尔可夫假设可能会受到限制。这种更高阶的网络表示不仅创建了基础复杂系统的更准确表示，而且还导致了更准确的网络分析。在本文中，我们首先提出一个可扩展且准确的模型BuildHON +，用于从复杂系统中获得具有不同顺序依赖关系的数据的高阶网络表示。然后，我们展示由BuildHON +建模的高阶网络表示 在识别异常方面比FON准确得多，这表明需要高阶网络表示和复杂系统建模来得出有意义的结论。