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An introduction to topological data analysis: fundamental and practical aspects for data scientists
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 …
data, identifying, extracting, and exploiting their underlying structure has become a problem …
Persistent homology analysis for materials research and persistent homology software: HomCloud
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 …
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
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 …
reduce data complexity and dimensionality is key to the performance of machine learning …
[PDF][PDF] Ripser. py: A lean persistent homology library for python
Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …
focused on understanding the shape and structure of data by computing topological …
Applications of topological data analysis in oncology
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 …
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
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 …
order encountered in colloidal assemblies is essential for several reasons. First of all, it is …
On the effectiveness of persistent homology
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 …
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
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 …
characterization of T1-weighted magnetic resonance (MR) images using two radiomics …
Functional summaries of persistence diagrams
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 …
and, more specifically, the persistence diagram. Persistence diagrams have also become …
Volume-optimal cycle: Tightest representative cycle of a generator in persistent homology
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 …
software for computing---volume-optimal cycles. Volume-optimal cycles are useful for …