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Approximating cycles in a shortest basis of the first homology group from point data
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dey, Tamal K. Sun, Jian Wang, Yusu |
| Copyright Year | 2011 |
| Abstract | Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper, we present an algorithm to compute a set of cycles from a point data that presumably sample a smooth manifold M ⊂ ℝ d . These cycles approximate a shortest basis of the first homology group H 1 (M) over coefficients in the finite field ℤ 2 . Previous results addressed the issue of computing the rank of the homology groups from point data, but there is no result on approximating the shortest basis of a manifold from its point sample. In arriving at our result, we also present a polynomial time algorithm for computing a shortest basis of H 1 (K) for any finite simplicial complex K whose edges have non-negative weights. |
| Starting Page | 124004 |
| Ending Page | 124004 |
| Page Count | 1 |
| File Format | PDF HTM / HTML |
| DOI | 10.1088/0266-5611/27/12/124004 |
| Volume Number | 27 |
| Alternate Webpage(s) | http://web.cse.ohio-state.edu/~tamaldey/paper/pcdloop/pcdloop.pdf |
| Alternate Webpage(s) | https://doi.org/10.1088/0266-5611%2F27%2F12%2F124004 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
