Predicting Persistence Diagrams

Topological data analysis (TDA) is a relatively new branch of data analysis. TDA methods find their application in many machine learning tasks, especially in those where information about the structure of objects is important. The main topological feature used in TDA is persistence diagrams (or their vectorization). However, the key problem in their use is the high computational complexity of obtaining them using deterministic algorithms. In our work, we will propose a method that will allow us to quickly obtain persistence diagrams for data of different modalities and various filter functions based on neural networks. We compare our approach with existing models for approximating persistence diagrams and functions of them in terms of both target metrics and quality on the classification task. The code, which we used to conduct experiments and instructions for reproducing them are available at the following link: https://github.com/ex7remum/Predicting_ Persistence_Diagrams