Notes on Applicability of Explainable AI Methods to Machine Learning Models Using Features Extracted by Persistent Homology

Data analysis that uses the output of topological data analysis as input for machine learning algorithms has been the subject of extensive research. This approach offers a means of capturing the global structure of data. Persistent homology (PH), a common methodology within the field of TDA, has found wide-ranging applications in machine learning. One of the key reasons for the success of the PH-ML pipeline lies in the deterministic nature of feature extraction conducted through PH. The ability to achieve satisfactory levels of accuracy with relatively simple downstream machine learning models, when processing these extracted features, underlines the pipeline's superior interpretability. However, it must be noted that this interpretation has encountered issues. Specifically, it fails to accurately reflect the feasible parameter region in the data generation process, and the physical or chemical constraints that restrict this process. Against this backdrop, we explore the potential application of explainable AI methodologies to this PH-ML pipeline. We apply this approach to the specific problem of predicting gas adsorption in metal-organic frameworks and demonstrate that it can yield suggestive results. The codes to reproduce our results are available at https://github.com/naofumihama/xai_ph_ml