A Topological Machine Learning Pipeline for Classification

TL;DR

This paper presents a topological machine learning pipeline that optimally associates Persistence Diagrams to digital data, enhancing classification performance through a systematic approach to data representation and filtration selection.

Contribution

It introduces a pipeline that automates the selection of filtrations and representation methods for Persistence Diagrams, improving topological data analysis in machine learning.

Findings

Pipeline determines optimal data representations for classification.

Comparison of representation methods on benchmark datasets.

First step towards a practical, easy-to-use topological ML pipeline.

Abstract

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.