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Questions tagged [topological-data-analysis]

Questions about persistent homology, computational topology, discrete morse theory, and applied algebraic topology in general.

Questions about persistent homology, computational topology, discrete morse theory, and applied algebraic topology in general. All things persistence theory belong here including those not directly related to data analysis applications.

Tag proposal can be viewed here. Proposals to separate any of the aforementioned topics into their own tags should be discussed in meta under the tag current tag management thread, provided that there are enough questions to justify the interest in a new tag.

122 questions
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Indecomposable Persistence Module

A persitence module is a functor $F:\mathbb{N} \rightarrow \mathbb{A}$ where $\mathbb{N}$ is the category of natural numbers with a partial order and $\mathbb{A}$ is some abelian category. There is a theorem by Crawley-Bovey that gives conditions on…
amd1234
  • 319
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Calculating Betti numbers in GUDHI

I am currently trying to write a program, which creates a simplicial complex, plots the persistence diagram and outputs the Betti numbers. I completed the first two steps using GUDHI, but I am not sure how can I compute Betti numbers using GUDHI or…
Anika
  • 11
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0-chain Boundary

Can anyone explain how adding two vertices in a connected graph to create a $0$-Chain is the boundary of some 1-dimensional chain? I know that the definition of boundary is the collection of $n+1$ faces, and each face is an $n-1$ simplice, but can…
LexyFidds
  • 47
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Computing Homology

I need A little bit more clarification when computing the homology of a chain complex. So the problem is: Compute the simplicial homology of the graph with vertices $$V=\left\{ 1, 2, 3, 4 \right\}$$ and edges $$E=\left \{ (1, 2)\right \}$$ Now, I…
LexyFidds
  • 47
0
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Is there a different barcode for the same filtration of complex?

The example at the beginning of the video https://youtu.be/qGkIuJmXhts, (Filtration of the example), I have a question about the barcode of a 1-dim persistent barcode. The video's author gave two homology bars, one born 2 died 5, and the other born…
Billal
  • 1
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1 answer

Persistent Homology of circular point data set

I was experimenting with simple data points like squares, rectangles, and polygons to forecast my 0D and 1D persistent homology. I'm having trouble predicting persistent homology in the case of a circle. I can figure out 0D persistent homology for…
Ashley Chraya
  • 51
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In persistent homology, when two homological features merge, how to determine which one dies?

Consider a W shaped function with local minimums at $y=1$ and $y=2$ and local maximum at $y=3$. When we look at the persistence diagram induced by the lower level sets of this function, Two topological features are born at $y=1$ and $y=2$ One of…
ThePortakal
  • 5,158
0
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Find an example of K, A, B, and I to show $\beta_i\neq \beta_i(A)+\beta_i(B)-\beta_i(A\cap B)$

I’ve been trying to find a simplicial complex $K$, where $A$ and $B$ are subcomplexes, and $K=A\cup B$ to show that the Betti number $\beta_i(K)\neq \beta_i(A)+\beta_i(B)-\beta_i(A\cap B)$ but every complex I come up with contradicts this for…
LexyFidds
  • 47