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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1803.10354 |
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| _version_ | 1866910499876110336 |
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| author | Janssen, Jeannette Ghandehari, Mahya |
| author_facet | Janssen, Jeannette Ghandehari, Mahya |
| contents | A square symmetric matrix is a Robinson similarity matrix if entries in its rows and columns are non-decreasing when moving towards the diagonal. A Robinson similarity matrix can be viewed as the affinity matrix between objects arranged in linear order, where objects closer together have higher affinity. We define a new parameter, $Γ_\max$, which measures how badly a given matrix fails to be Robinson similarity. Namely, a matrix is Robinson similarity precisely when its $Γ_\max$ attains zero, and a matrix with small $Γ_\max$ is close (in the normalized $\ell^1$-norm) to a Robinson similarity matrix. Moreover, both $Γ_\max$ and the Robinson similarity approximation can be computed in polynomial time. Thus, our parameter recognizes Robinson similarity matrices which are perturbed by noise, and can therefore be a useful tool in the problem of seriation of noisy data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_10354 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An optimization parameter for seriation of noisy data Janssen, Jeannette Ghandehari, Mahya Combinatorics A square symmetric matrix is a Robinson similarity matrix if entries in its rows and columns are non-decreasing when moving towards the diagonal. A Robinson similarity matrix can be viewed as the affinity matrix between objects arranged in linear order, where objects closer together have higher affinity. We define a new parameter, $Γ_\max$, which measures how badly a given matrix fails to be Robinson similarity. Namely, a matrix is Robinson similarity precisely when its $Γ_\max$ attains zero, and a matrix with small $Γ_\max$ is close (in the normalized $\ell^1$-norm) to a Robinson similarity matrix. Moreover, both $Γ_\max$ and the Robinson similarity approximation can be computed in polynomial time. Thus, our parameter recognizes Robinson similarity matrices which are perturbed by noise, and can therefore be a useful tool in the problem of seriation of noisy data. |
| title | An optimization parameter for seriation of noisy data |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1803.10354 |