Reviews: Deep Learning with Topological Signatures

This paper proposes a deep neural network model to learn from persistence diagrams extracted from data. A persistence diagram is a 2D point sets describing the topological information of a given data in the view of a chosen scalar function. While a diagram describes useful global information of the data, existing learning methods [25,18] only use it in a kernel-based setting. The key contribution of this paper is to construct an input layer for persistence diagrams. This is non-trivial as persistence diagrams behave very differently from traditional vectorized features (non-Euclidean metric).