Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances tend to not reflect semantic similarities well. This renders unsupervised tasks, such as clustering, difficult when working with the latent representations. We demonstrate that taking the geometry of the generative model into account is sufficient to make simple clustering algorithms work well over latent representations. Leaning on the recent finding that deep generative models constitute stochastically immersed Riemannian manifolds, we propose an efficient algorithm for computing geodesics (shortest paths) and computing distances in the latent space, while taking its distortion into account. We further propose a new architecture for modeling uncertainty in variational autoencoders, which is essential for understanding the geometry of deep generative models. Experiments show that the geodesic distance is very likely to reflect the internal structure of the data.

该论文提出了一种考虑生成模型的几何特性的算法，它可以使得在潜变量表示中使用简单的聚类算法更加有效，同时提出了一种新的用于建模变分自编码器中不确定性的架构。实验表明，此算法能够反映数据的内部结构。

深度生成模型中的测地线聚类