Concept

Finsler manifold

Related publications (38)

Isometry groups of non-positively curved spaces: Discrete subgroups

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour throu ...

2009

Image alignment with rotation manifolds built on sparse geometric expansions

Pascal Frossard, Effrosyni Kokiopoulou

In this paper we discuss the problem of alignment of patterns under arbitrary rotation. When a generic image pattern is geometrically transformed, it typically spans a (possibly nonlinear) manifold in a high dimensional space. When the pattern of interest ...

2007

Orthogonal Neighborhood Preserving Projections: A projection-based dimensionality reduction technique

Effrosyni Kokiopoulou

This paper considers the problem of dimensionality reduction by orthogonal projection techniques. The main feature of the proposed techniques is that they attempt to preserve both the intrinsic neighborhood geometry of the data samples and the global geome ...

2007

Orthogonal Neighborhood Preserving Projections

Effrosyni Kokiopoulou

Orthogonal Neighborhood Preserving Projections (ONPP) is a linear dimensionality reduction technique which attempts to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. The proposed technique constructs a weight ...

IEEE2005

Planar arrangement of high-dimensional biomedical data sets by isomap coordinates

Daniel Thalmann, Sofiane Sarni, Pablo Stanislaw De Heras Ciechomski, Ik Soo Lim

This article addresses 2-dimensional layout of high-dimensional biomedical datasets, which is useful for browsing them efficiently We employ the isomap technique, which is based on classical MDS (multi-dimensional scaling) but seeks to preserve the intrins ...

IEEE2003

Planar arrangement of high-dimensional biomedical data sets by Isomap coordinates

Daniel Thalmann, Sofiane Sarni, Pablo Stanislaw De Heras Ciechomski, Ik Soo Lim

This article addresses 2-dimensional layout of high-dimensional biomedical datasets, which is useful for browsing them efficiently. We employ the Isomap technique, which is based on classical MDS (multi-dimensional scaling) but seeks to preserve the intrin ...

Institute of Electrical and Electronics Engineers Computer Society2003

Planar arrangement of high-dimensional biomedical data sets by isomap coordinates

Daniel Thalmann, Sofiane Sarni, Pablo Stanislaw De Heras Ciechomski

IEEE2003

Replacement manifolds: A method to uniformize semiclassical wave functions

Jiri Vanicek

We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor o ...

2001

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