  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.
