Riemannian manifold learning.
IEEE Trans Pattern Anal Mach Intell
; 30(5): 796-809, 2008 May.
Article
en En
| MEDLINE
| ID: mdl-18369250
ABSTRACT
Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, i.e., how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low-dimensional space. Experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings.
Texto completo:
1
Colección:
01-internacional
Banco de datos:
MEDLINE
Asunto principal:
Algoritmos
/
Reconocimiento de Normas Patrones Automatizadas
/
Inteligencia Artificial
/
Interpretación de Imagen Asistida por Computador
/
Imagenología Tridimensional
Tipo de estudio:
Diagnostic_studies
Idioma:
En
Revista:
IEEE Trans Pattern Anal Mach Intell
Asunto de la revista:
INFORMATICA MEDICA
Año:
2008
Tipo del documento:
Article
País de afiliación:
China