# A Topological Machine Learning Pipeline for Classification

arXiv: https://arxiv.org/abs/2309.15276 · HTML: https://mlsanity.com/paper/2309.15276/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 26 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [A Topological "Reading" Lesson: Classification of MNIST using TDA](https://mlsanity.com/paper/1910.08345/) (2019)
- [A Kernel for Multi-Parameter Persistent Homology](https://mlsanity.com/paper/1809.10231/) (2018)

## Built on by (most cited first, 1 of 1)

- [Image Classification using Combination of Topological Features and Neural Networks](https://mlsanity.com/paper/2311.06375/) (2023)

## Abstract (arXiv)

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation methods and parameters. The development of such a topological pipeline for Machine Learning involves two crucial steps that strongly affect its performance: firstly, digital data must be represented as an algebraic object with a proper associated filtration in order to compute its topological summary, the Persistence Diagram. Secondly, the persistence diagram must be transformed with suitable representation methods in order to be introduced in a Machine Learning algorithm. We assess the performance of our pipeline, and in parallel, we compare the different representation methods on popular benchmark datasets. This work is a first step toward both an easy and ready-to-use pipeline for data classification using persistent homology and Machine Learning, and to understand the theoretical reasons why, given a dataset and a task to be performed, a pair (filtration, topological representation) is better than another.