Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this proximity-preserving strategy: Graph topology patterns, while preserved well into an embedding manifold by preserving proximity, may distort in the ambient embedding Euclidean space, and hence to detect them becomes difficult for machine learning models. To address the problem, we propose curvature regularization, to enforce flatness for embedding manifolds, thereby preventing the distortion. We present a novel angle-based sectional curvature, termed ABS curvature, and accordingly three kinds of curvature regularization to induce flat embedding manifolds during graph embedding. We integrate curvature regularization into five popular proximity-preserving embedding methods, and empirical results in two applications show significant improvements on a wide range of open graph datasets.

中文翻译：

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曲率正则化以防止图形嵌入失真

图嵌入的最新研究已在各种应用中取得成功。大多数图嵌入方法会将图的接近度保留到嵌入空间中的流形中。我们讨论了关于这种邻近性保留策略的一个重要但被忽略的问题：图拓扑模式虽然通过保留邻近性而很好地保留在嵌入流形中，但可能会在周围的嵌入欧几里德空间中变形，因此很难为机器学习模型检测它们。为了解决该问题，我们提出曲率正则化，以增强用于嵌入歧管的平面度，从而防止变形。我们提出了一种新颖的基于角度的截面曲率，称为ABS曲率，并相应地提供了三种曲率正则化，以在图形嵌入过程中引入平坦的嵌入歧管。