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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10900 |
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| _version_ | 1866912147417595904 |
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| author | Arias-Castro, Ery Vishwanath, Siddharth |
| author_facet | Arias-Castro, Ery Vishwanath, Siddharth |
| contents | Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical scaling, and then the remaining nodes are recursively embedded by lateration. A graph is a lateration graph when it can be embedded by such a procedure. We provide a stability result for a particular variant of sequential lateration. We do so in a setting where the dissimilarities represent noisy Euclidean distances between nodes in a geometric lateration graph. We then deduce, as a corollary, a perturbation bound for stress minimization. To argue that our setting applies broadly, we show that a (large) random geometric graph is a lateration graph with high probability under mild conditions, extending a previous result of Aspnes et al (2006). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10900 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of Sequential Lateration and of Stress Minimization in the Presence of Noise Arias-Castro, Ery Vishwanath, Siddharth Statistics Theory Networking and Internet Architecture Probability Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical scaling, and then the remaining nodes are recursively embedded by lateration. A graph is a lateration graph when it can be embedded by such a procedure. We provide a stability result for a particular variant of sequential lateration. We do so in a setting where the dissimilarities represent noisy Euclidean distances between nodes in a geometric lateration graph. We then deduce, as a corollary, a perturbation bound for stress minimization. To argue that our setting applies broadly, we show that a (large) random geometric graph is a lateration graph with high probability under mild conditions, extending a previous result of Aspnes et al (2006). |
| title | Stability of Sequential Lateration and of Stress Minimization in the Presence of Noise |
| topic | Statistics Theory Networking and Internet Architecture Probability |
| url | https://arxiv.org/abs/2310.10900 |