Sanity Check for Persistence Diagrams

Recently many efforts have been made to incorporate persistence diagrams, one of major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we propose a sanity check for persistence diagrams to delineate critical values and pairings of critical values (structure of persistence module). For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over summaries based on merely critical values. Our results help provide insights on when persistence diagram based summaries could be more suitable.