The Wasserstein metric between #PersistenceDiagrams can be easily extended to #MergeTrees by restricting the set of candidate assignments to partial isomorphisms 👇
https://arxiv.org/abs/2207.10960

Available in the #TopologyToolKit!

#TopologicalDataAnalysis #DataScience #Visualization

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Check out the new #TopologyToolKit Example Website!
Dozens of #TopologicalDataAnalysis pipelines.
Today, learn how to extract persistent 1-cycles in the cosmic web from #Astrophysics in 39 lines of #Python 👇
https://topology-tool-kit.github.io/examples/persistentGenerators_darkSky/

#Visualization #DataScience #Machinelearning

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

To compute #PersistentHomology, one needs to check, for each d-simplex σi of a filtration, if it "fills" a (d-1)-dimensional hole, i.e. if its boundary ∂σi is homologous to a non-trivial (d-1)-cycle created on an unpaired (d-1)-simplex (blue).
👇
https://arxiv.org/abs/2206.13932

#TopologicalDataAnalysis #Visualization #DataScience

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Need to analyze a collection of datasets based on their #MergeTrees?
Check out our new approach for Principal Geodesic Analysis in the Wasserstein metric space of #MergeTrees, with applications to dimension reduction 👇
https://arxiv.org/abs/2207.10960

#TopologicalDataAnalysis #Visualization #DataScience

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Check out the new #TopologyToolKit Example Website!
Dozens of #TopologicalDataAnalysis pipelines.
🧑‍🎓Today, learn how to extract persistent 1-cycles in high-dimensional data in 63 lines of #Python👇
https://topology-tool-kit.github.io/examples/persistentGenerators_periodicPicture/
#DataScience #Machinelearning

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Under mild conditions, at the step i of the filtration of a d-dimensional simplicial complex K, the Betti number β(d−k-1) of Ki (top) is equal to the Betti number β(k) of the dual of the complement of Ki (bottom).

https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Under mild conditions, at the step i of the filtration of a d-dimensional simplicial complex K, the Betti number β(d−k-1) of Ki (top) is equal to the Betti number β(k) of the dual of the complement of Ki (bottom).

https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Under mild conditions, at the step i of the filtration of a d-dimensional simplicial complex K, the Betti number β(d−k-1) of Ki (top) is equal to the Betti number β(k) of the dual of the complement of Ki (bottom).

https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Check out the new #TopologyToolKit Example Website!
Dozens of #TopologicalDataAnalysis pipelines.

Today, learn how to cluster datasets with intricate structures based on their #PersistenceDiagrams in 85 lines of #Python

https://topology-tool-kit.github.io/examples/clusteringKelvinHelmholtzInstabilities/
#DataScience #Machinelearning

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Two p-cycles a and b are "homologous" (i.e. belong to the same #Homology class) if there exists a (p+1)-chain c, such that b = a + ∂c (mod-2 sum)
👇
https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis #TopologyToolKit #PersistentHomology #Visualization #DataScience #MachineLearning

Need to analyze a collection of datasets based on their #PersistenceDiagrams?
Check out our new approach for Principal Geodesic Analysis in the Wasserstein space of #PersistenceDiagrams, with applications to dimension reduction:
https://arxiv.org/abs/2207.10960
#TopologicalDataAnalysis #Visualization #DataScience #MachineLearing #TopologyToolKit
Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Check out our new paper with
@_gosiao
on the #TopologicalDataAnalysis of magnetic currents in molecules with the #TopologyToolKit 👇
Accepted to
@PCCP
https://arxiv.org/abs/2212.08690
#PersistentHomology #visualization #compchem #paraview

Checkout the new #TopologyToolKit Example Website!
Dozens of #TopologicalDataAnalysis pipelines.
🧑‍🎓Today, learn how to compute the #Wasserstein distance between the #PersistenceDiagrams of two datasets in 48 lines of #Python👇
https://topology-tool-kit.github.io/examples/persistenceDiagramDistance/
#DataScience #Machinelearning

Announcement: our lightning fast ⚡️ approach for #PersistenceDiagram computation has been accepted to IEEE TVCG!
Available in the #TopologyToolKit!
Details and benchmarks 👇
https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis #datascience #visualization #machinelearning #python

Topological persistence is an importance measure in #PersistentHomology, with a strong practical utility for noise removal in various applications: #Imaging, #Clustering, #ClimateScience, #Geophysics, #MaterialScience and more! 👇
https://arxiv.org/pdf/2206.13932
#TopologicalDataAnalysis

Need to analyze a collection of datasets based on their topological signatures?
Checkout our new #IEEETVCG paper on Principal Geodesics of merge trees and persistence diagrams:
https://arxiv.org/abs/2207.10960
Already in the #TopologyToolKit!
#TopologicalDataAnalysis #Visualization #DataScience #machinelearning

Referenced link: https://topoinvis-workshop.github.io/2022/program.html
Originally posted by IEEE VIS / @ieeevis@twitter.com: https://twitter.com/JulienTierny/status/1578243446023675904#m

RT by @ieeevis: 📢 Join us at the IEEE Workshop on Topological Data Analysis and Visualization, held in conjunction with @ieeevis.
The fantastic @robertghrist will give the keynote!
More details there 👇
https://topoinvis-workshop.github.io/2022/program.html
#visualization #TopologicalDataAnalysis #datascience #topology

RT @JulienTierny
📢 Please spread the word:
This year, we have multiple research positions open in #TopologicalDataAnalysis!
We're hiring:
- 2 Ph.D. students
- 1 post-doc
- 1 engineer
If you are passionate about computer science, maths and data, come and work with us :)
https://erc-tori.github.io/jobs/