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Mathematics > Statistics Theory
Title: Stability of Sequential Lateration and of Stress Minimization in the Presence of Noise
(Submitted on 17 Oct 2023 (v1), last revised 26 Mar 2024 (this version, v2))
Abstract: 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).
Submission history
From: Ery Arias-Castro [view email][v1] Tue, 17 Oct 2023 00:18:56 GMT (22kb)
[v2] Tue, 26 Mar 2024 19:13:00 GMT (198kb,D)
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