# Computing Multidimensional Persistence

@article{Carlsson2009ComputingMP, title={Computing Multidimensional Persistence}, author={Gunnar E. Carlsson and Gurjeet Singh and Afra Zomorodian}, journal={ArXiv}, year={2009}, volume={abs/0907.2423} }

The theory of multidimensional persistence captures the topology of a multifiltration --- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a polynomial time algorithm for computing multidimensional persistence.

## 71 Citations

Invariants for Multidimensional Persistence

- Computer Science
- 2015

The amount of data that our digital society collects is unprecedented. This represents a valuable opportunity to improve our quality of life by gaining insights about complex problems related to ne…

Multidimensional Persistence and Noise

- Mathematics, Computer ScienceFound. Comput. Math.
- 2017

The feature counting invariant is introduced and it is proved that assigning this invariant to compact tame functors is a 1-Lipschitz operation.

An Introduction to Multiparameter Persistence

- MathematicsArXiv
- 2022

In topological data analysis (TDA), one often studies the shape of data by constructing a ﬁltered topological space, whose structure is then examined using persistent homology. However, a single…

Necessary conditions for discontinuities of multidimensional persistent Betti numbers

- Mathematics
- 2015

Topological persistence has proven to be a promising framework for dealing with problems concerning the analysis of data. In this context, it was originally introduced by taking into account…

Computing Multipersistence by Means of Spectral Systems

- Mathematics, Computer ScienceISSAC
- 2019

This paper shows that spectral sequences and persistent homology are related, generalizing results valid in the case of filtrations over \Z, and develops a new module for the Kenzo system computing multipersistence.

A new approximation Algorithm for the Matching Distance in Multidimensional Persistence

- Computer Science
- 2011

This paper proposes a new computational framework to deal with the multidimensional matching distance, by proving some new theoretical results and using them to formulate an algorithm for computing such a distance up to an arbitrary threshold error.

P-persistent homology of finite topological spaces

- MathematicsArXiv
- 2015

It is shown that for any reasonable P-persistent object X in the category of finite topological spaces, there is a P− weighted graph, whose clique complex has the same P-Persistent homology as X.

Reducing complexes in multidimensional persistent homology theory

- Computer ScienceJ. Symb. Comput.
- 2017

Generalized Persistence Algorithm for Decomposing Multi-parameter Persistence Modules

- Computer ScienceJournal of Applied and Computational Topology
- 2022

A generalization of the persistence algorithm based on a generalized matrix reduction technique that runs in $O(n^{2\omega})$ time where $\omega<2.373$ is the exponent for matrix multiplication.

Morse-based Fibering of the Persistence Rank Invariant

- MathematicsArXiv
- 2020

It is shown how discrete Morse theory may be used to compute the rank invariant, proving that it is completely determined by its values at points whose coordinates are critical with respect to a discrete Morse gradient vector field.

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