A dimension reduction scheme for the computation of optimal unions of subspaces
Given a set of points F in a high dimensional space, the problem of finding a union of subspaces U_i V_i ⊆ R^N that best explains the data F increases dramatically with the dimension of R^N. In this article, we study a class of transformations that map the problem into another one in lower dimension...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/117502 |
| Acceso en línea: | http://hdl.handle.net/11336/117502 |
| Access Level: | acceso abierto |
| Palabra clave: | SPARSITY PROJECTIVE CLUSTERING DIMENSIONALITY REDUCTION RANDOM MATRICES CONCENTRATION INEQUALITIES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Given a set of points F in a high dimensional space, the problem of finding a union of subspaces U_i V_i ⊆ R^N that best explains the data F increases dramatically with the dimension of R^N. In this article, we study a class of transformations that map the problem into another one in lower dimension. We use the best model in the low dimensional space to approximate the best solution in the original high dimensional space. We then estimate the error produced between this solution and the optimal solution in the high dimensional space. |
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