Discovering connectivity patterns of directed networks is a crucial step to understand complex systems such as brain-, social-, and financial networks. Several existing network topology inference approaches rely on structural equation models (SEMs). These presume that exogenous inputs are available, which may be unrealistic in certain applications. Recently, an alternative line of work reformulated SEM-based topology identification as a three-way tensor decomposition task. This way, knowing the exogenous input correlation statistics (rather than the exogenous inputs themselves) suffices for network topology identification. The downside is that this approach is computationally expensive. In addition, it is hard to incorporate prior information of the network structure (e.g., sparsity and local smoothness) into this framework, while such prior information may help enhance performance when handling real-world noisy data. The present work puts forth a joint diagonalizaition (JD)-based approach to directed network topology inference. JD can be viewed as a variant of tensor decomposition, but features more efficient algorithms, and can readily account for the network structure. Different from existing alternatives, novel identifiability guarantees are derived regardless of the exogenous inputs or their statistics. Three JD algorithms tailored for network topology inference are developed, and their performance is showcased using simulated and real data tests.

中文翻译：

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通过相关矩阵的联合对角线化对有向图进行拓扑识别

发现定向网络的连通性模式是理解复杂系统（如大脑，社交和金融网络）的关键步骤。现有的几种网络拓扑推断方法都依赖于结构方程模型（SEM）。这些假定存在外部输入，这在某些应用程序中可能是不现实的。最近，另一种工作方式将基于SEM的拓扑标识重新构造为三向张量分解任务。这样，了解外部输入相关性统计信息（而不是外部输入本身）就足以进行网络拓扑识别。缺点是这种方法在计算上很昂贵。另外，很难将网络结构的先验信息（例如，稀疏性和局部平滑度）合并到此框架中，这些先验信息可能有助于提高处理实际嘈杂数据时的性能。目前的工作提出了联合对角线化基于（JD）的定向网络拓扑推断方法。JD可以看作是张量分解的一种变体，但具有更高效的算法，并且可以轻松说明网络结构。与现有的替代方法不同，无论外部输入或其统计数据如何，都得出了新颖的可识别性保证。开发了针对网络拓扑推断量身定制的三种JD算法，并通过模拟和真实数据测试展示了它们的性能。