Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data space. Although real-world data is often acquired in settings where relationships are influenced by a priori known rules, such domain knowledge is still not well exploited in structure inference problems. In this paper, we identify the structure of signals defined in a data space whose inner relationships are encoded by multi-layer graphs. We aim at properly exploiting the information originating from each layer to infer the global structure underlying the signals. We thus present a novel method for combining the multiple graphs into a global graph using mask matrices, which are estimated through an optimization problem that accommodates the multi-layer graph information and a signal representation model. The proposed mask combination method also estimates the contribution of each graph layer in the structure of signals. The experiments conducted both on synthetic and real-world data suggest that integrating the multi-layer graph representation of the data in the structure inference framework enhances the learning procedure considerably by adapting to the quality and the quantity of the input data.

中文翻译：

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用于全局结构推断的多层图的蒙版组合

结构推断是数据科学中网络数据处理和分析的重要任务。近年来，已经开发了许多方法来学习在数据空间中捕获的一组观察结果基础的图结构。尽管现实世界中的数据通常是在关系受先验已知规则影响的环境中获取的，但在结构推断问题中仍无法很好地利用此类领域知识。在本文中，我们确定在数据空间中定义的信号结构，其内部关系由多层图编码。我们旨在适当地利用源自每一层的信息来推断信号基础的全局结构。因此，我们提出了一种使用遮罩矩阵将多个图组合成全局图的新颖方法，它们是通过优化问题来估算的，该问题包含了多层图形信息和信号表示模型。所提出的掩模组合方法还估计每个图形层在信号结构中的贡献。在合成和真实数据上进行的实验表明，将数据的多层图形表示集成到结构推断框架中，可以通过适应输入数据的质量和数量来大大提高学习过程。