Topological data analysis (TDA) has already provided many novel insights into machine learning (Carrière et al., 2020) due to its capabilities of synthesizing the shape information into a multiset of points in two dimensions: the persistence diagrams (Wasserman, 2016).
Furthermore, many researchers in the field hope to give new insights into deep-learning models by applying TDA techniques to study the models’ weights, the activation values in the different layers, and their evolution during the training phase (Naitzat et al., 2020). Orthogonally, TDA techniques have been used as feature engineering tools to extract novel information from the data, which are then used as standard features in a machine learning pipeline, with significant success in many fields (Hensel et al., 2021).
