The Euler characteristic: A general topological descriptor for complex data

Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under study. Topology is an area of mathematics provides diverse tools to characterize data objects. In this work, we study a specific tool known as Euler characteristic (EC). The EC general, low-dimensional, and interpretable descriptor topological spaces defined by We revise foundations highlight its connections with statistics, linear algebra, field theory, graph theory. discuss advantages offered use in characterization complex datasets; do so, illustrate different applications interest chemical engineering such process monitoring, flow cytometry, microscopy. show effectively reduces datasets reduction facilitates tasks visualization, regression, classification, clustering.