@article{conti_topological_2022, 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.}, author = {Conti, Francesco and Moroni, Davide and Pascali, Maria Antonietta}, date = {2022-08-27}, doi = {10.3390/math10173086}, issn = {2227-7390}, journaltitle = {Mathematics}, keywords = {1 - Digit recognition, 1 - Dynamical systems, 1 - Graph classification, 1 - Images, 1 - Machine learning, 1 - Spectral data analysis, 2 - Persistence images, 2 - Persistent homology, 3 - Grayscale images, 3 - Linked twisted map}, langid = {english}, number = {17}, pages = {3086}, shortjournal = {Mathematics}, title = {A Topological Machine Learning Pipeline for Classification}, url = {https://www.mdpi.com/2227-7390/10/17/3086}, urldate = {2022-11-30}, volume = {10} }