| dc.contributor | GUSTAVO RODRIGUEZ GOMEZ | |
| dc.creator | FABRICIO OTONIEL PEREZ PEREZ | |
| dc.date | 2013-01 | |
| dc.date.accessioned | 2023-07-25T16:21:14Z | |
| dc.date.available | 2023-07-25T16:21:14Z | |
| dc.identifier | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/271 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7805491 | |
| dc.description | In many research areas, such as computer vision, image processing, pattern recognition,
or systems identification, the segmentation of heterogeneous high-dimensional data sets is
one of the most common and important tasks. Based on the subspace clustering approach,
the Generalized Principal Component Analysis (GPCA) is an algebraic-geometric method
that attempts to perform this task. However, due to GPCA requires performing matrix
decompositions whose computational cost is cubic with respect to the size of the matrix (in
the worst case), the data segmentation becomes expensive when such size is very large.
Consequently, the present thesis work is intended to support our initial hypothesis: it
is possible to find matrix decompositions via randomized schemes that not only reduce
the computational costs, but also they maintain the effectiveness of their results. This
allows GPCA to manipulate both large and heterogeneous high-dimensional data sets, and
thus GPCA can enter into domains where its applicability has been partially or totally
restricted. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Instituto Nacional de Astrofísica, Óptica y Electrónica | |
| dc.relation | citation:Perez-Perez F.O. | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | info:eu-repo/classification/Análisis de los datos/Data analysis | |
| dc.subject | info:eu-repo/classification/Reducción de datos/Data reduction | |
| dc.subject | info:eu-repo/classification/Algoritmos determinísticos/Deterministic algorithms | |
| dc.subject | info:eu-repo/classification/Algoritmos aleatorios/Randomized algorithms | |
| dc.subject | info:eu-repo/classification/Subespacio agrupación/Subspace clustering | |
| dc.subject | info:eu-repo/classification/Aproximación polinomial/Polynomial approximation | |
| dc.subject | info:eu-repo/classification/Álgebra lineal numérica/Numerical linear algebra | |
| dc.subject | info:eu-repo/classification/Valor singular de descomposición/Singular value decomposition | |
| dc.subject | info:eu-repo/classification/Métodos Monte Carlo/Monte Carlo methods | |
| dc.subject | info:eu-repo/classification/Análisis de componentes principales/Principal component analysis | |
| dc.subject | info:eu-repo/classification/cti/1 | |
| dc.subject | info:eu-repo/classification/cti/12 | |
| dc.subject | info:eu-repo/classification/cti/1203 | |
| dc.subject | info:eu-repo/classification/cti/1203 | |
| dc.title | Improving the efficiency of algebraic subspace clustering through randomized low-rank matrix approximations | |
| dc.type | info:eu-repo/semantics/masterThesis | |
| dc.type | info:eu-repo/semantics/acceptedVersion | |
| dc.audience | students | |
| dc.audience | researchers | |
| dc.audience | generalPublic | |
