将图信号翻译推断为分类任务的不变变换
Inferring Graph Signal Translations as Invariant Transformations for Classification Tasks
摘要：
图形信号处理（GSP）领域已经提出了将谐波分析推广到通过图形表示的复杂域的工具。在这些工具中，翻译是定义许多其他工具所必需的。大多数作品建议仅使用图结构（即边缘）来定义翻译。这样的问题一般是不适定的，因为图传达了关于邻域的信息，而不是关于方向的信息。在本文中，我们提出将翻译推断为边缘约束操作，使用深度学习框架使监督分类问题保持不变。因此，我们的方法使用图结构和标记信号来推断翻译。我们进行实验与常规的2D图像和抽象的超链接网络，以显示所提出的方法的有效性，在推断有意义的翻译支持图上的信号。
英文摘要：
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to define translations using solely the graph structure (i.e. edges). Such a problem is ill-posed in general as a graph conveys information about neighborhood but not about directions. In this paper, we propose to infer translations as edge-constrained operations that make a supervised classification problem invariant using a deep learning framework. As such, our methodology uses both the graph structure and labeled signals to infer translations. We perform experiments with regular 2D images and abstract hyperlink networks to show the effectiveness of the proposed methodology in inferring meaningful translations for signals supported on graphs.
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