Título
Improving the efficiency of algebraic subspace clustering through randomized low-rank matrix approximations
Autor
FABRICIO OTONIEL PEREZ PEREZ
Colaborador
GUSTAVO RODRIGUEZ GOMEZ (Asesor de tesis)
Nivel de Acceso
Acceso Abierto
Materias
Data analysis - (ANÁLISIS DE LOS DATOS) Data reduction - (REDUCCIÓN DE DATOS) Deterministic algorithms - (ALGORITMOS DETERMINÍSTICOS) Randomized algorithms - (ALGORITMOS ALEATORIOS) Subspace clustering - (SUBESPACIO AGRUPACIÓN) Polynomial approximation - (APROXIMACIÓN POLINOMIAL) Numerical linear algebra - (ÁLGEBRA LINEAL NUMÉRICA) Singular value decomposition - (VALOR SINGULAR DE DESCOMPOSICIÓN) Monte Carlo methods - (MÉTODOS MONTE CARLO) Principal component analysis - (ANÁLISIS DE COMPONENTES PRINCIPALES) CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA - (CTI) MATEMÁTICAS - (CTI) CIENCIA DE LOS ORDENADORES - (CTI)
Resumen o descripción
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.
Editor
Instituto Nacional de Astrofísica, Óptica y Electrónica
Fecha de publicación
enero de 2013
Tipo de publicación
Tesis de maestría
Versión de la publicación
Versión aceptada
Recurso de información
Formato
application/pdf
Idioma
Inglés
Audiencia
Estudiantes
Investigadores
Público en general
Sugerencia de citación
Perez-Perez F.O.
Repositorio Orígen
Repositorio Institucional del INAOE
Descargas
276