论文标题
用于图形嵌入的计算可拖动的riemannian歧管
Computationally Tractable Riemannian Manifolds for Graph Embeddings
论文作者
论文摘要
将图表示为某些弯曲的riemannian歧管中的节点嵌入的集合最近由于其理想的几何感应偏见，例如，层次结构受益于高压几何学，因此在机器学习方面已获得动力。但是，超越了嵌入恒定曲率的嵌入空间，虽然潜在的表现力更强大，但事实证明是具有挑战性的，因为人们很容易失去计算可拖动工具的吸引力，例如地球距离或riemannian梯度。在这里，我们探索了计算高效的矩阵歧管，展示了如何学习和优化这些riemannian空间中的图形嵌入。从经验上讲，我们表现出对欧几里得几何形状的一致改进，同时经常基于捕获不同图形性能的各种指标来超过双曲线和椭圆形嵌入。我们的结果是机器学习管道中非欧国人嵌入的好处的新证据。
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic geometry. However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore computationally efficient matrix manifolds, showcasing how to learn and optimize graph embeddings in these Riemannian spaces. Empirically, we demonstrate consistent improvements over Euclidean geometry while often outperforming hyperbolic and elliptical embeddings based on various metrics that capture different graph properties. Our results serve as new evidence for the benefits of non-Euclidean embeddings in machine learning pipelines.
