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

arXiv: https://arxiv.org/abs/2310.09780 · HTML: https://mlsanity.com/paper/2310.09780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Computing the Testing Error without a Testing Set](https://mlsanity.com/paper/2005.00450/) (2020)
- [Explaining black box decisions by Shapley cohort refinement](https://mlsanity.com/paper/1911.00467/) (2019)
- [A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them](https://mlsanity.com/paper/2305.09536/) (2023)
- [Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homology](https://mlsanity.com/paper/1712.05103/) (2017)
- [A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification](https://mlsanity.com/paper/1908.06856/) (2019)
- [A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science](https://mlsanity.com/paper/2207.10552/) (2022)
- [Dark soliton detection using persistent homology](https://mlsanity.com/paper/2107.14594/) (2021)
- [Topological Representations of Local Explanations](https://mlsanity.com/paper/2201.02155/) (2022)

## Abstract (arXiv)

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