🍩 Database of Original & Non-Theoretical Uses of Topology

1. A Topological Machine Learning Pipeline for Classification (2022)

   Francesco Conti, Davide Moroni, Maria Antonietta Pascali

   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.

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   • Digit recognition
   • Dynamical systems
   • Graph classification
   • Images
   • Machine learning
   • Spectral data analysis
   • Grayscale images
   • Linked twisted map
   • Persistence images
   • Persistent homology