Lost without a compass: Nonmetric triangulation and landmark multidimensional scaling
Mark A. Davenport · 2013
Suppose that we wish to determine the location of a point x* ∈ ℝkby comparing the distance from x* to various points x1, x2, ..., xkℝkwith known position. In this paper we consider the scenario where we are only provided with (possibly noisy or contradictory) relations of the form ∥x* - xi∥2j∥2. We propose a simple algorithm that uses convex optimization techniques to estimate x* from such data and we provide simulations demonstrating its effectiveness in practice.