Separating Topological Noise from Features Using Persistent Entropy

@article{Atienza2016SeparatingTN,
  title={Separating Topological Noise from Features Using Persistent Entropy},
  author={Nieves Atienza and Roc{\'i}o Gonz{\'a}lez-D{\'i}az and Matteo Rucco},
  journal={ArXiv},
  year={2016},
  volume={abs/1605.02885}
}
In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy. 
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Persistent entropy for separating topological features from noise in vietoris-rips complexes
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This paper presents new important properties of persistent entropy of Vietoris-Rips filtrations, and derives a simple method for separating topological noise from features in Vietoris -Rips Filtrations.
A density-based approach to feature detection in persistence diagrams for firn data
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This work constructs a new, automated approach for identifying persistence diagram points that represent robust long-life features that may be used to provide a more accurate estimate of Betti numbers for the underlying space.
Data Analysis Methods using Persistence Diagrams
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A new distance is introduced on the space of persistence diagrams, and it is shown that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem.
Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams
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A nonparametric way to estimate the global probability density function for a random persistence diagram and it is proved that the associated kernel density estimate converges to the true distribution as the number of persistence diagrams increases and the bandwidth shrinks accordingly.
Persistent homology for object segmentation in multidimensional grayscale images
Topology-based fluorescence image analysis for automated cell identification and segmentation
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It is demonstrated that topological data analysis can provide accurate segmentation of arbitrarily-shaped cells, offering a means for automatic and objective data extraction.
Persistent Homology: Hole Detection in LiDAR Point Clouds with Topological Data Analysis by Suen
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  • Environmental Science
  • 2021
Laser scanning has been widely used in various applications because of its efficiency and accuracy. However, a common problem found in laser scanning is that there are holes contained in the point…

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