论文标题
用Rie-Sne可视化Riemannian数据
Visualizing Riemannian data with Rie-SNE
论文作者
论文摘要
在产生数据平面视图时，属于歧管上数据的数据的忠实可视化必须考虑到基本的几何形状。在本文中，我们将经典的随机邻居嵌入（SNE）算法扩展到一般的Riemannian歧管的数据。我们用riemannian扩散对应物代替标准高斯假设，并提出有效的近似值，仅需要访问riemannian距离和体积的计算。我们证明该方法还允许将数据从一个流形映射到另一个歧管，例如从高维球到低维球。
Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.
