# A Topological Data Analysis Based Classifier

arXiv: https://arxiv.org/abs/2111.05214 · HTML: https://mlsanity.com/paper/2111.05214/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 74 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [A persistence landscapes toolbox for topological statistics](https://mlsanity.com/paper/1501.00179/) (2014)
- [The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes](https://mlsanity.com/paper/2001.02581/) (2020)
- [giotto-ph: A Python Library for High-Performance Computation of Persistent Homology of Vietoris-Rips Filtrations](https://mlsanity.com/paper/2107.05412/) (2021)
- [Persistent Homology of Attractors For Action Recognition](https://mlsanity.com/paper/1603.05310/) (2016)
- [Generalized Penalty for Circular Coordinate Representation](https://mlsanity.com/paper/2006.02554/) (2020)
- [An Efficient Representation for Filtrations of Simplicial Complexes](https://mlsanity.com/paper/1607.08449/) (2016)
- [Building Efficient and Compact Data Structures for Simplicial Complexes](https://mlsanity.com/paper/1503.07444/) (2015)
- [Classification based on Topological Data Analysis](https://mlsanity.com/paper/2102.03709/) (2021)

## Built on by (most cited first, 2 of 2)

- [A topological classifier to characterize brain states: When shape matters more than variance](https://mlsanity.com/paper/2303.04231/) (2023)
- [Prototype Selection Using Topological Data Analysis](https://mlsanity.com/paper/2511.04873/) (2025)

## Abstract (arXiv)

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes an algorithm that applies TDA directly to multi-class classification problems, without any further ML stage, showing advantages for imbalanced datasets. The proposed algorithm builds a filtered simplicial complex on the dataset. Persistent Homology (PH) is applied to guide the selection of a sub-complex where unlabeled points obtain the label with the majority of votes from labeled neighboring points. We select 8 datasets with different dimensions, degrees of class overlap and imbalanced samples per class. On average, the proposed TDABC method was better than KNN and weighted-KNN. It behaves competitively with Local SVM and Random Forest baseline classifiers in balanced datasets, and it outperforms all baseline methods classifying entangled and minority classes.