An introduction to topological data analysis: fundamental and practical aspects for data scientists

F Chazal, B Michel - Frontiers in artificial intelligence, 2021‏ - frontiersin.org
With the recent explosion in the amount, the variety, and the dimensionality of available
data, identifying, extracting, and exploiting their underlying structure has become a problem …

Persistent homology analysis for materials research and persistent homology software: HomCloud

I Obayashi, T Nakamura, Y Hiraoka - journal of the physical society of …, 2022‏ - journals.jps.jp
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 …

Persistent-homology-based machine learning: a survey and a comparative study

CS Pun, SX Lee, K **a - Artificial Intelligence Review, 2022‏ - Springer
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 …

[PDF][PDF] Ripser. py: A lean persistent homology library for python

C Tralie, N Saul, R Bar-On - Journal of Open Source Software, 2018‏ - joss.theoj.org
Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …

Applications of topological data analysis in oncology

A Bukkuri, N Andor, IK Darcy - Frontiers in artificial intelligence, 2021‏ - frontiersin.org
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 …

[HTML][HTML] Pattern detection in colloidal assembly: A mosaic of analysis techniques

V Lotito, T Zambelli - Advances in colloid and interface science, 2020‏ - Elsevier
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 …

On the effectiveness of persistent homology

R Turkes, GF Montufar, N Otter - Advances in Neural …, 2022‏ - proceedings.neurips.cc
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 …

Hepatic tumor classification using texture and topology analysis of non-contrast-enhanced three-dimensional T1-weighted MR images with a radiomics approach

A Oyama, Y Hiraoka, I Obayashi, Y Saikawa, S Furui… - Scientific reports, 2019‏ - nature.com
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 …

Functional summaries of persistence diagrams

E Berry, YC Chen, J Cisewski-Kehe… - Journal of Applied and …, 2020‏ - Springer
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 …

Volume-optimal cycle: Tightest representative cycle of a generator in persistent homology

I Obayashi - SIAM Journal on Applied Algebra and Geometry, 2018‏ - SIAM
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 …