Learning random points from geometric graphs or orderings
Let Xv for v∈V be a family of n iid uniform points in the square (Formula presented.). Suppose first that we are given the random geometric graph (Formula presented.), where vertices u and v are adjacent when the Euclidean distance dE(Xu,Xv) is at most r. Let n3/14≪r≪n1/2. Given G (without geometric...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/329582 |
| Acceso en línea: | https://hdl.handle.net/2117/329582 https://dx.doi.org/10.1002/rsa.20922 |
| Access Level: | acceso abierto |
| Palabra clave: | Machine learning Graph theory Approximate embedding Random geometric graphs Unit disk graphs Vertex orders Aprenentatge automàtic Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Sumario: | Let Xv for v∈V be a family of n iid uniform points in the square (Formula presented.). Suppose first that we are given the random geometric graph (Formula presented.), where vertices u and v are adjacent when the Euclidean distance dE(Xu,Xv) is at most r. Let n3/14≪r≪n1/2. Given G (without geometric information), in polynomial time we can with high probability approximately reconstruct the hidden embedding, in the sense that “up to symmetries,” for each vertex v we find a point within distance about r of Xv; that is, we find an embedding with “displacement” at most about r. Now suppose that, instead of G we are given, for each vertex v, the ordering of the other vertices by increasing Euclidean distance from v. Then, with high probability, in polynomial time we can find an embedding with displacement (Formula presented.). |
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