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## 108 Citations

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- 2020

It is shown that multiparameter landscapes are stable with respect to the interleaving distance and persistence weighted Wasserstein distance, and that the collection of multiparameters landscapes faithfully represents the rank invariant.

The Persistence Landscape and Some of Its Properties

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Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an…

Persistent Homology: Functional Summaries of Persistence Diagrams for Time Series Analysis

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It is proved that the results reflected on the dependency relationship between persistence landscapes functional norms and variance-covariance for multivariate time series embedded via the sliding window method are valid for time series understanding them as a realization of a weakly stationary stochastic process.

Scalar Field Comparison with Topological Descriptors

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This work presents a state-of-the-art report on scalar field comparison using topological descriptors and provides a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time-varying fields, and ensembles.

Kernel Method for Persistence Diagrams via Kernel Embedding and Weight Factor

- Computer ScienceJ. Mach. Learn. Res.
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A kernel method on persistence diagrams is proposed that allows one to control the effect of persistence, and, if necessary, noisy topological properties can be discounted in data analysis.

Topological Data Analysis for Object Data

- Computer Science
- 2018

A framework for using persistence landscapes to vectorize object data and perform statistical analysis is presented and the most persistent features are shown to be “topological noise” and the statistical analysis depends on the less persistent features which are referred to as the “geometric signal”.

Persistent homology detects curvature

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- 2020

It is proved that persistent homology detects the curvature of disks from which points have been sampled, and a general computational framework for solving inverse problems using the average persistence landscape, a continuous mapping from metric spaces with a probability measure to a Hilbert space is described.

Topological spaces of persistence modules and their properties

- MathematicsJ. Appl. Comput. Topol.
- 2018

This work considers various classes of persistence modules, including many of those that have been previously studied, and describes the relationships between them, and undertake a systematic study of the resulting topological spaces and their basic topological properties.

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