# Topological Quality of Subsets via Persistence Matching Diagrams

arXiv: https://arxiv.org/abs/2306.02411 · HTML: https://mlsanity.com/paper/2306.02411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Builds on (most cited first, 10 of 10)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Shallow decision trees for explainable k-means clustering](https://mlsanity.com/paper/2112.14718/) (2021)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [Topology-based Representative Datasets to Reduce Neural Network Training Resources](https://mlsanity.com/paper/1903.08519/) (2019)
- [Partial Matchings Induced by Morphisms between Persistence Modules](https://mlsanity.com/paper/2107.04519/) (2021)
- [On the Choice of Data for Efficient Training and Validation of End-to-End Driving Models](https://mlsanity.com/paper/2206.00608/) (2022)

## Abstract (arXiv)

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques. Specifically, we define the persistence matching diagram, a topological invariant derived from combining embeddings with persistent homology. We provide an algorithm to compute it using minimum spanning trees. Also, the invariant allows us to understand whether the subset ``represents well" the clusters from the larger dataset or not, and we also use it to estimate bounds for the Hausdorff distance between the subset and the complete dataset. In particular, this approach enables us to explain why the chosen subset is likely to result in poor performance of a supervised learning model.