A Topological Machine Learning Pipeline for Classification

Francesco Conti (), Davide Moroni and Maria Antonietta Pascali
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Francesco Conti: Department of Mathematics, University of Pisa, 56126 Pisa, Italy
Davide Moroni: Institute of Information Science and Technologies “A. Faedo”, National Research Council of Italy (CNR), 56124 Pisa, Italy
Maria Antonietta Pascali: Institute of Information Science and Technologies “A. Faedo”, National Research Council of Italy (CNR), 56124 Pisa, Italy

Mathematics, 2022, vol. 10, issue 17, 1-33

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.

Keywords: topological machine learning; persistent homology; classification; vectorization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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