Comments (1)
Thanks for the kind words, it means a lot!
Sadly the algorithm in question will not work in higher dimensions. It works by first building the 1-skeleton of the simplicial complex at the specified time as a graph. Then, it goes through each edge in the cocycle and connects its endpoints with the shortest path (ignoring the edges of the cocycle). Finally, it selects the one with the minimum weight and returns it (this is what best_sx
and best_path
are).
The problem here is that we don't have a nice analog to a shortest path in higher dimensions.
It might also be worth noting that in general, finding optimal representative cycles in dimensions higher than one is a very hard problem. If I'm not mistaken, the problem of finding the "shortest" representatives is NP-hard. However, I have a hunch that there is an efficient way to get sufficiently nice cycles according to some other metric. This is definitely something I want to explore in the future.
Also, note that this cycle reconstruction feature is very experimental. I agree the code is a bit convoluted and It also has some serious performance issues. I will probably rewrite it later this year when I have more time to work on this stuff again. I'll try to add some comments to the code in the meantime.
By the way, involuted homology (ripserer(...; alg=:involuted)
) has no problem working in high dimensions but it computes an arbitrary cycle. Maybe that can be of some use to you?
from ripserer.jl.
Related Issues (15)
- TagBot trigger issue HOT 33
- Cubical PH on a torus HOT 2
- Performance advice HOT 1
- bad promote_rule HOT 1
- Option to supply SparseCSCMatrix of distances directly HOT 1
- Error when reconstructing cycles HOT 1
- Can Ripserer compute the discrete morse theory for a simplex, or compute the collapses? HOT 1
- On keeping track on merges? HOT 2
- On multithreading support? HOT 2
- slow computation for a custom filtration of depth 1 (simplicial complex) HOT 2
- incorrect implementation of prime field $\mathbb{Z}/p$ when p is large HOT 3
- Obtaining the simplicial complex for a given threshold HOT 1
- Codecov migration to marketplace app
- [JOSS] Add section to the README and DOCS about related efforts in Julia HOT 2
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from ripserer.jl.