Services on Demand
Journal
Article
Indicators
Cited by SciELO
Access statistics
Related links
Cited by Google
Similars in SciELO
Similars in Google
Share
Revista Colombiana de Estadística
Print version ISSN 0120-1751
Abstract
PEREZ, RAÚL ALBERTO and GONZALEZ-FARIAS, GRACIELA. Regresión de mínimos cuadrados parciales sobre matrices simétricas definidas positiva. Rev.Colomb.Estad. [online]. 2013, vol.36, n.1, pp.177-192. ISSN 0120-1751.
Recently there has been an increased interest in the analysis of different types of manifold-valued data, which include data from symmetric positive-definite 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.
Keywords : Matrix theory; Multicollinearity; Regression; Riemann\linebreak manifold.