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Confidence regions for a persistence diagram of a single image with one or more loops
Susan Glenn, Jessi Cisewski-Kehe, Jun Zhu +1
Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics o…
Tracking Temporal Evolution of Topological Features in Image Data
Susan Glenn, Jessi Cisewski-Kehe, Jun Zhu +1
Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). Ho…
MaxTDA: Robust Statistical Inference for Maximal Persistence in Topological Data Analysis
Sixtus Dakurah, Jessi Cisewski-Kehe
Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are…
A Subsequence Approach to Topological Data Analysis for Irregularly-Spaced Time Series
Sixtus Dakurah, Jessi Cisewski-Kehe
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topo…