École Nationale Supérieure de
Techniques Avancées

Abstract

Topological Data Analysis (TDA) is a field of data science whose goal is to detect and encode topological features (such as connected components, loops, cavities...) that are present in datasets in order to improve inference and prediction. The main descriptor of TDA is called the persistence diagram and a common vector representation of those diagrams are persistence images. The main problem of persistence diagram, and thus persistence images is that they can take time to compute. During this internship, the goal was to build a neural network that is able to predict persistence images given a point cloud. In a second phase, we will see how a this neural network can be extended thank to variational autoencoders (VAE). VAE is one of the most popular approaches to unsupervised learning of complicated distribution. The goal behind using a VAE is to predict, not only a persistence image, but a joint distribution between a point cloud and its persistence image, in order to solve the inverse problem which is to go back to a space from a persistence image.