# Questions tagged [topological-data-analysis]

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

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### Persistence Vector Spaces

I am currently reading Gunnar Carlsson's "Topological Pattern Recognition for Point Cloud Data", you can find it here: http://math.stanford.edu/~gunnar/actanumericathree.pdf I have a ...
1 vote
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### Can you do geometry with persistent homology?

Setup In practice, persistent homology of data $X$ is often used to infer the homology of the underlying (Riemannian) manifold $M$ that the data is sampled from. However most filtrations (Vietoris, ...
1 vote
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### Isoparametric function on hypersurfaces in Euclidean space

A isoparametric function $f$ on a Riemannian manifold is a function that satisfies the followings identities: $|\nabla f|=a(f)$ and $\Delta f=b(f)$. Now, I would like to deal with hypersurfaces in the ...
42 views

### Short exact sequence of persistence modules

I am currently trying to work out a elementary proof of the following statement: Let $X$ be a simplicial complex with a filtration $\mathbb{X}: X=\bigcup_{n\in\mathbb{N}} X_n$, let $k\in\mathbb{N}$ ...
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### Why are giotto-tda and cripser giving different persistent diagrams?

When I find the persistence diagrams using cubical homology and using the natural grayscale filtration of the image, I get two different answers depending on the package I use. By inspection, it seems ...
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### How much more efficiently can one compute persistent homology after restricting the point cloud's shape?

Topological data analysis employs topology to study discrete multidimensional data sets. One often treats these data as point clouds embedded in $\mathbb{R}^n$. And in practice, it may be hard to ...
86 views

### Introducing myself to discrete Morse theory

I plan to write my maths masters' dissertation on discrete Morse theory. I intend to write it from a theoretical point of view, relating it to classical Morse theory. I still have to decide exactly ...
92 views

### 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 ...
100 views

### Why is the following a cubical complex

The german Wikipedia-page on cubical complexes has the following example for a cubical complex. I don't understand how the 45° rotated square on the right is the product of elementary intervals. As I ...