#topologicaldataanalysis — Public Fediverse posts

R Consortium-funded tooling for TDA in R: statistical inference for persistence diagrams

Persistence diagrams are great summaries of “shape in data” (persistent homology) — but many workflows stop at plotting. The {inphr} package goes further: statistical inference for samples of persistence diagrams, aimed at comparing populations of diagrams across data types.

Read: https://r-consortium.org/posts/statistical-inference-for-persistence-diagrams/

#rstats #TDA #TopologicalDataAnalysis #PersistentHomology #Statistics #DataScience #OpenSource

Here's a step-by-step guide on how to analyze multiple time series. https://hackernoon.com/how-to-analyze-multiple-time-series-a-step-by-step-guide #topologicaldataanalysis

#TopologicalDataAnalysis shows how #GeneExpression shaped the form & function of flowering #plants over 125 million years of #evolution, providing a novel way to explore complex biological data. #dataviz @bob_vanburen &co in #PLOSBiology https://plos.io/4actz9N

📢Announcement: we're happy to announce the release 1.2 of the #TopologyToolKit! 🎉
Downloads: https://topology-tool-kit.github.io/downloads.html
Examples: https://topology-tool-kit.github.io/examples/
Checkout the ChangeLog 👇
https://github.com/topology-tool-kit/ttk/releases/tag/1.2.0
#TopologicalDataAnalysis #datascience #visualization #machinelearning #python

@abuseofnotation There are at least two reasons that categories aren't usually covered during an introduction to abstract algebra.

1) While the modern upper-level undergraduate curriculum does push a lot more abstraction than appeared a century ago, this is still balanced with the psychological need for students to not go up too many levels too quickly. Even though categories are some kind of algebraic structure generalizing groups and lattices, the standard examples are categories of other mathematical objects one has already studed (sets, groups, etc.). For students this is conceptually quite different from the more concrete situation of finite symmetry groups, for example.

2) The applications of categories (separately from the special cases of groups/lattices/monoids/posets/etc.) don't yet appear enough for the average person with a bachelor's in math to need to know them. This may change as #AppliedCategoryTheory, #TopologicalDataAnalysis, #FunctionalProgramming, and so forth continue to mature and have greater impacts outside of academia.

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/
#Visualization #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/)

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

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

For @3CardMonteCarloMethodMan

Thanks for the follow David.

The fifth #collage is for you.

#Dogs #Politics #TopologicalDataAnalysis #Baseball #AdventureCycling #Al #SpaceScience #Humor #Mathematics

#followcollage #art #community #fedi #freshstart #aiart #communityart #sharing

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