# Classification based on Topological Data Analysis

arXiv: https://arxiv.org/abs/2102.03709 · HTML: https://mlsanity.com/paper/2102.03709/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 7 Feb 2021.

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

- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Topological Approaches to Deep Learning](https://mlsanity.com/paper/1811.01122/) (2018)
- [The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes](https://mlsanity.com/paper/2001.02581/) (2020)
- [Persistent Homology of Attractors For Action Recognition](https://mlsanity.com/paper/1603.05310/) (2016)
- [An Efficient Representation for Filtrations of Simplicial Complexes](https://mlsanity.com/paper/1607.08449/) (2016)
- [The Compressed Annotation Matrix: an Efficient Data Structure for Computing Persistent Cohomology](https://mlsanity.com/paper/1304.6813/) (2013)
- [Building Efficient and Compact Data Structures for Simplicial Complexes](https://mlsanity.com/paper/1503.07444/) (2015)
- [A topological data analysis based classification method for multiple measurements](https://mlsanity.com/paper/1904.02971/) (2019)

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

- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)
- [A topological classifier to characterize brain states: When shape matters more than variance](https://mlsanity.com/paper/2303.04231/) (2023)

## 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, even imbalanced datasets, without any further ML stage. The proposed algorithm built a filtered simplicial complex on the dataset. Persistent homology is then applied to guide choosing a sub-complex where unlabeled points obtain the label with most votes from labeled neighboring points. To assess the proposed method, 8 datasets were selected with several degrees of class entanglement, variability on the samples per class, and dimensionality. On average, the proposed TDABC method was capable of overcoming baseline classifiers (wk-NN and k-NN) in each of the computed metrics, especially on classifying entangled and minority classes.