论文标题
通过多维缩放的球形图
Spherical Graph Drawing by Multi-dimensional Scaling
论文作者
论文摘要
我们描述了一种有效且可扩展的球形图嵌入方法。该方法使用欧几里得应力函数的概括，用于适合球形空间的多维缩放缩放，在该空间中，采用了地球成对距离而不是欧几里得距离。通过随机梯度下降优化了所得的球形应力功能。定量和定性评估证明了该方法的可扩展性和有效性。我们还表明，与欧几里得和双曲线空间相比，某些图家族可以在球体上嵌入较低的变形。
We describe an efficient and scalable spherical graph embedding method. The method uses a generalization of the Euclidean stress function for Multi-Dimensional Scaling adapted to spherical space, where geodesic pairwise distances are employed instead of Euclidean distances. The resulting spherical stress function is optimized by means of stochastic gradient descent. Quantitative and qualitative evaluations demonstrate the scalability and effectiveness of the proposed method. We also show that some graph families can be embedded with lower distortion on the sphere, than in Euclidean and hyperbolic spaces.
