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 ∪ iV 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....
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_Aldroubi |
| Aporte de: |
| id |
todo:paper_15306429_v10_n1-2_p135_Aldroubi |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_15306429_v10_n1-2_p135_Aldroubi2023-10-03T16:21:15Z A dimension reduction scheme for the computation of optimal unions of subspaces Aldroubi, A. Anastasio, M. Cabrelli, C. Molter, U. Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪ iV 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. © 2011 SAMPLING PUBLISHING. Fil:Anastasio, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_Aldroubi |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity |
| spellingShingle |
Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity Aldroubi, A. Anastasio, M. Cabrelli, C. Molter, U. A dimension reduction scheme for the computation of optimal unions of subspaces |
| topic_facet |
Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity |
| description |
Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪ iV 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. © 2011 SAMPLING PUBLISHING. |
| format |
JOUR |
| author |
Aldroubi, A. Anastasio, M. Cabrelli, C. Molter, U. |
| author_facet |
Aldroubi, A. Anastasio, M. Cabrelli, C. Molter, U. |
| author_sort |
Aldroubi, A. |
| title |
A dimension reduction scheme for the computation of optimal unions of subspaces |
| title_short |
A dimension reduction scheme for the computation of optimal unions of subspaces |
| title_full |
A dimension reduction scheme for the computation of optimal unions of subspaces |
| title_fullStr |
A dimension reduction scheme for the computation of optimal unions of subspaces |
| title_full_unstemmed |
A dimension reduction scheme for the computation of optimal unions of subspaces |
| title_sort |
dimension reduction scheme for the computation of optimal unions of subspaces |
| url |
http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_Aldroubi |
| work_keys_str_mv |
AT aldroubia adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT anastasiom adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT cabrellic adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT molteru adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT aldroubia dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT anastasiom dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT cabrellic dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT molteru dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces |
| _version_ |
1807322776251400192 |