Partial least squares regression on symmetric positive-definite matrices Reportar como inadecuado




Partial least squares regression on symmetric positive-definite matrices - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.



Recently there has been an increased interest in the analysis of differenttypes of manifold-valued data, which include data from symmetric positivedefinitematrices. In many studies of medical cerebral image analysis, amajor concern is establishing the association among a set of covariates andthe manifold-valued data, which are considered as responses for characterizingthe shapes of certain subcortical structures and the differences betweenthem.The manifold-valued data do not form a vector space, and thus, it is notadequate to apply classical statistical techniques directly, as certain operationson vector spaces are not defined in a general Riemannian manifold. Inthis article, an application of the partial least squares regression methodologyis performed for a setting with a large number of covariates in a euclideanspace and one or more responses in a curved manifold, called a Riemanniansymmetric space. To apply such a technique, the Riemannian exponentialmap and the Riemannian logarithmic map are used on a set of symmetricpositive-definite matrices, by which the data are transformed into a vectorspace, where classic statistical techniques can be applied. The methodologyis evaluated using a set of simulated data, and the behavior of the techniqueis analyzed with respect to the principal component regression.

Tipo de documento: Artículo - Article

Palabras clave: Matrix theory, Multicollinearity, Regression, Riemann manifold





Fuente: http://www.bdigital.unal.edu.co


Introducción



Revista Colombiana de Estadística Junio 2013, volumen 36, no.
1, pp.
177 a 192 Partial Least Squares Regression on Symmetric Positive-Definite Matrices Regresión de mínimos cuadrados parciales sobre matrices simétricas definidas positiva Raúl Alberto Pérez1,a , Graciela González-Farias2,b 1 Escuela de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Medellín, Colombia 2 Departamento de Probabilidad y Estadística, CIMAT-México Unidad Monterrey, Monterrey Nuevo León, México Resumen Recently there has been an increased interest in the analysis of different types of manifold-valued data, which include data from symmetric positivedefinite matrices.
In many studies of medical cerebral image analysis, a major concern is establishing the association among a set of covariates and the manifold-valued data, which are considered as responses for characterizing the shapes of certain subcortical structures and the differences between them. The manifold-valued data do not form a vector space, and thus, it is not adequate to apply classical statistical techniques directly, as certain operations on vector spaces are not defined in a general Riemannian manifold.
In this article, an application of the partial least squares regression methodology is performed for a setting with a large number of covariates in a euclidean space and one or more responses in a curved manifold, called a Riemannian symmetric space.
To apply such a technique, the Riemannian exponential map and the Riemannian logarithmic map are used on a set of symmetric positive-definite matrices, by which the data are transformed into a vector space, where classic statistical techniques can be applied.
The methodology is evaluated using a set of simulated data, and the behavior of the technique is analyzed with respect to the principal component regression. Palabras clave: Matrix theory, Multicollinearity, Regression, Riemann manifold. a Assistant b Associate Professor.
E-mail: raper...






Documentos relacionados