# Prototype Selection Using Topological Data Analysis

arXiv: https://arxiv.org/abs/2511.04873 · HTML: https://mlsanity.com/paper/2511.04873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 79 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Distributed Representations of Sentences and Documents](https://mlsanity.com/paper/1405.4053/) (2014)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Dissimilarity-based Sparse Subset Selection](https://mlsanity.com/paper/1407.6810/) (2014)
- [DTM-based Filtrations](https://mlsanity.com/paper/1811.04757/) (2018)
- [SPOT: A framework for selection of prototypes using optimal transport](https://mlsanity.com/paper/2103.10159/) (2021)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [Classification of Imbalanced Data with a Geometric Digraph Family](https://mlsanity.com/paper/1904.04564/) (2019)
- [Computing multiparameter persistent homology through a discrete Morse-based approach](https://mlsanity.com/paper/1811.05396/) (2018)
- [Singular value decomposition based matrix surgery](https://mlsanity.com/paper/2302.11446/) (2023)
- [Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH](https://mlsanity.com/paper/2310.16437/) (2023)
- [A topological data analysis based classification method for multiple measurements](https://mlsanity.com/paper/1904.02971/) (2019)
- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)

## Abstract (arXiv)

Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data. This paper introduces two different persistence-based prototype selector variants, Topological Prototype Selector (TPS) and Boundary-Conscious Topological Prototype Selector (BoundaryTPS). TPS uses two sequential Rips filtrations to retain boundary-relevant and interior-typical points. BoundaryTPS is a single-stage variant whose vertex-weighted filtration concentrates retention near the decision boundary. We evaluate both methods against seven classical baselines on fifteen real datasets and find that the topological methods occupy a different operating point in the prototype-selection design space than existing methods. BoundaryTPS achieves the lowest mean Friedman rank on H1 persistence-diagram preservation and is significantly better than five of the seven baselines (Nemenyi, α = 0.05). TPS ranks third on the same endpoint. Both methods are more stable under fold perturbation than any chained-decision selector tested, and both inherit the source set's class proportions without label-aware machinery. On aggregate G-Mean both methods are competitive but not leading, with rank-1 frequencies of 11.3% (TPS) and 9.9% (BoundaryTPS) across fold combinations. Empirically, both methods scale sub-quadratically in sample size.