# The Ring of Algebraic Functions on Persistence Bar Codes

@article{Adcock2013TheRO, title={The Ring of Algebraic Functions on Persistence Bar Codes}, author={Aaron B. Adcock and Erik Carlsson and Gunnar E. Carlsson}, journal={arXiv: Rings and Algebras}, year={2013} }

We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.

## 112 Citations

### Persistent homology and applied homotopy theory

- Mathematics
- 2020

This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence…

### Computational Tools in Weighted Persistent Homology

- MathematicsChinese Annals of Mathematics, Series B
- 2017

In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted…

### Tropical Coordinates on the Space of Persistence Barcodes

- Computer ScienceFound. Comput. Math.
- 2019

The purpose of this paper is to identify tropical coordinates on the space of barcodes and prove that they are stable with respect to the bottleneck distance and Wasserstein distances.

### Tropical Coordinates on the Space of Persistence Barcodes

- Computer Science
- 2016

The purpose of this paper is to identify tropical coordinates on the space of barcodes and prove that they are stable with respect to the bottleneck distance and Wasserstein distances.

### Further Properties and Applications of Weighted Persistent Homology

- Mathematics
- 2017

In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for…

### Persistence Paths and Signature Features in Topological Data Analysis

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2020

A new feature map for barcodes as they arise in persistent homology computation that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks.

### Amplitudes on abelian categories

- Mathematics
- 2021

The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one…

### Stratifying the space of barcodes using Coxeter complexes

- Mathematics
- 2021

We use tools from geometric group theory to produce a stratification of the space Bn of barcodes with n bars. The top-dimensional strata are indexed by permutations associated to barcodes as defined…

### Curvature Sets Over Persistence Diagrams

- Mathematics
- 2021

We study an invariant of compact metric spaces which combines the notion of curvature sets introduced by Gromov in the 1980s together with the notion of VietorisRips persistent homology. For given…

### Vectorization of persistence barcode with applications in pattern classification of porous structures

- Computer ScienceComput. Graph.
- 2020

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