Manifold-valued Dirichlet Processes.
JMLR Workshop Conf Proc
; 2015: 1199-1208, 2015 07.
Article
in En
| MEDLINE
| ID: mdl-26973982
ABSTRACT
Statistical models for manifold-valued data permit capturing the intrinsic nature of the curved spaces in which the data lie and have been a topic of research for several decades. Typically, these formulations use geodesic curves and distances defined locally for most cases - this makes it hard to design parametric models globally on smooth manifolds. Thus, most (manifold specific) parametric models available today assume that the data lie in a small neighborhood on the manifold. To address this 'locality' problem, we propose a novel nonparametric model which unifies multivariate general linear models (MGLMs) using multiple tangent spaces. Our framework generalizes existing work on (both Euclidean and non-Euclidean) general linear models providing a recipe to globally extend the locally-defined parametric models (using a mixture of local models). By grouping observations into sub-populations at multiple tangent spaces, our method provides insights into the hidden structure (geodesic relationships) in the data. This yields a framework to group observations and discover geodesic relationships between covariates X and manifold-valued responses Y, which we call Dirichlet process mixtures of multivariate general linear models (DP-MGLM) on Riemannian manifolds. Finally, we present proof of concept experiments to validate our model.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Type of study:
Risk_factors_studies
Language:
En
Journal:
JMLR Workshop Conf Proc
Year:
2015
Document type:
Article
Affiliation country: