Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …

Abstract Characterization of the morphology, identification of patterns and quantification of
order encountered in colloidal assemblies is essential for several reasons. First of all, it is …

The emergence of the information age in the last few decades brought with it an explosion of
biomedical data. But with great power comes great responsibility: there is now a pressing …

The purpose of this study is to evaluate the accuracy for classification of hepatic tumors by
characterization of T1-weighted magnetic resonance (MR) images using two radiomics …

One of the primary areas of interest in applied algebraic topology is persistent homology,
and, more specifically, the persistence diagram. Persistence diagrams have also become …

The present paper shows a mathematical formalization of---as well as algorithms and
software for computing---volume-optimal cycles. Volume-optimal cycles are useful for …

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis.
Even though PH has been used in many different types of applications, the reasons behind …