Name
Abstract | ||
|---|---|---|
In this paper, we focus on the problem of point-to-set classification, where single points are matched against sets of correlated points. Since the points commonly lie in Euclidean space while the sets are typically modeled as elements on Riemannian manifold, they can be treated as Euclidean points and Riemannian points respectively. To learn a metric between the heterogeneous points, we propose a novel Euclidean-to-Riemannian metric learning framework. Specifically, by exploiting typical Riemannian metrics, the Riemannian manifold is first embedded into a high dimensional Hilbert space to reduce the gaps between the heterogeneous spaces and meanwhile respect the Riemannian geometry of the manifold. The final distance metric is then learned by pursuing multiple transformations from the Hilbert space and the original Euclidean space (or its corresponding Hilbert space) to a common Euclidean subspace, where classical Euclidean distances of transformed heterogeneous points can be measured. Extensive experiments clearly demonstrate the superiority of our proposed approach over the state-of-the-art methods. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/CVPR.2014.217 | CVPR |
Keywords | Field | DocType |
euclidean-to-riemannian metric learning framework,riemannian geometry,euclidean-to-riemannian metric learning,point-to-set classification, euclidean-to-riemannian metric learning,point-to-set classification,hilbert spaces,learning (artificial intelligence),euclidean space,correlated points,riemannian manifold,heterogeneous points,image classification,heterogeneous spaces,riemannian points,high dimensional hilbert space,euclidean points,manifolds,hilbert space,learning artificial intelligence,geometry,kernel | Riemannian manifold,Artificial intelligence,Statistical manifold,Fundamental theorem of Riemannian geometry,Pseudo-Riemannian manifold,Information geometry,Topology,Fisher information metric,Pattern recognition,Euclidean distance,Pure mathematics,Euclidean space,Mathematics | Conference |
ISSN | Citations | PageRank |
1063-6919 | 32 | 0.81 |
References | Authors | |
30 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhiwu Huang | 1 | 252 | 15.26 |
| Ruiping Wang | 2 | 894 | 41.60 |
| Shiguang Shan | 3 | 6322 | 283.75 |
| Xilin Chen | 4 | 6291 | 306.27 |