Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which includes weighted graphs, distance matrices, and kernel matrices. We prove that the encoder embedding satisfies the law of large numbers and the central limit theorem on a per-observation basis. Under certain condition, it achieves asymptotic normality on a per-class basis, enabling optimal classification through discriminant analysis. These theoretical findings are validated through a series of experiments involving weighted graphs, as well as text and image data transformed into general graph representations using appropriate distance metrics.

翻译：图编码器嵌入是图数据领域的一项新兴技术，能够以快速且可扩展的方式从二值图中生成顶点级表示。本文将该方法的适用范围扩展至通用图模型，涵盖加权图、距离矩阵与核矩阵。我们证明编码器嵌入在逐观测意义上满足大数定律与中心极限定理。在特定条件下，该方法能在逐类别意义上达到渐近正态性，从而通过判别分析实现最优分类。这些理论发现通过一系列实验得到验证，实验涉及加权图，以及通过适当距离度量转化为通用图表示的文本与图像数据。