Dimension Reduction of Two-Dimensional Persistence via Distance Deformations
Maximilian Neumann
TL;DR
This paper presents a novel method for simplifying two-dimensional persistent homology by transforming time data into distances, aiding in the analysis of RNA virus time series datasets.
Contribution
It introduces a new distance deformation technique to reduce 2D persistence to 1D, enhancing analysis of time series in biological data.
Findings
Effective reduction of 2D persistence to 1D.
Improved analysis of RNA virus datasets.
Potential applications in biological data analysis.
Abstract
This article grew out of the application part of my Master's thesis at the Faculty of Mathematics and Information Science at Ruprecht-Karls-Universit\"at Heidelberg under the supervision of PD Dr. Andreas Ott. In the context of time series analyses of RNA virus datasets with persistent homology, this article introduces a new method for reducing two-dimensional persistence to one-dimensional persistence by transforming time information into distances.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Bioinformatics and Genomic Networks · Cell Image Analysis Techniques