A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Visualizing bregman voronoi diagrams

2007
*
Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07
*

Generalizing

doi:10.1145/1247069.1247089
dblp:conf/compgeom/NielsenBN07
fatcat:do7vrdsztrdctpaxbnjbf7pfji
*Voronoi**Diagrams**Voronoi**diagrams*widely studied in comp. geometry [AK'00]: Abstract*Voronoi**diagrams*[Klein'89], etc. ...*diagram*equivalence classes Since Vor(S; d 2 ) = Vor(S; d 2 2 ), the ordinary*Voronoi**diagram*is interpreted as a*Bregman**Voronoi**diagram*. ... Nock On*Bregman**Voronoi**Diagrams*, straight and geodesic triangulations are the same ordinary Delaunay triangulations.) F. Nielsen, J.-D. Boissonnat and R. Nock On*Bregman**Voronoi**Diagrams*...##
###
Quantum Voronoi diagrams and Holevo channel capacity for 1-qubit quantum states

2008
*
2008 IEEE International Symposium on Information Theory
*

We show that these

doi:10.1109/isit.2008.4594955
dblp:conf/isit/NielsenN08
fatcat:5pe5nltwhfhdraktmfkqoen4t4
*diagrams*can be computed as*Bregman**Voronoi**diagrams*for the corresponding*Bregman*generator acting on Hermitian density matrices. ... This implies that these dual*diagrams*can be derived from power*diagrams*of balls in the Laguerre geometry, and allows one to prove by equivalence that the von Neumann quantum*Voronoi**diagram*on the degenerated ... Theorem 3.1: The von Neumann quantum*Voronoi**diagrams*are*Bregman**Voronoi**diagrams*that can be computed from equivalent power*diagrams*. ...##
###
Bregman Voronoi Diagrams

2010
*
Discrete & Computational Geometry
*

We also introduce extensions of these

doi:10.1007/s00454-010-9256-1
fatcat:lik3travqzdfhbm2md3p2t5mfi
*diagrams*, e.g., k-order and k-bag*Bregman**Voronoi**diagrams*, and introduce*Bregman*triangulations of a set of points and their connection with*Bregman**Voronoi**diagrams*... Accordingly,*Bregman**Voronoi**diagrams*allow one to define information-theoretic*Voronoi**diagrams*in statistical parametric spaces based on the relative entropy of distributions. ... Fig. 2 2*Visualizing*the*Bregman*divergence. ...##
###
Skew Jensen-Bregman Voronoi Diagrams
[chapter]

2011
*
Lecture Notes in Computer Science
*

This paper includes novel extensions to matrix-based Jensen-

doi:10.1007/978-3-642-25249-5_4
fatcat:7eclqfkzjbexbdosy3vc6kgtzm
*Bregman*divergences, and present the general framework of skew Jensen-*Bregman**Voronoi**diagrams*that include*Bregman**Voronoi**diagrams*as particular ... We study the geometric properties and combinatorial complexities of both the*Voronoi**diagrams*and the centroidal*Voronoi**diagrams*induced by such as class of divergences. ... Namely, the (normalized) skew Jensen-*Bregman**Voronoi**diagrams*become a regular*Bregman**Voronoi**diagram*[6] . Figure 9 depicts several skew left-sided/right-sided Jensen-*Bregman**Voronoi**diagrams*. ...##
###
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
[article]

2007
*
arXiv
*
pre-print

We also introduce extensions of these

arXiv:0709.2196v1
fatcat:7juz25kny5fi3g45qkag3c4xze
*diagrams*, e.g. k-order and k-bag*Bregman**Voronoi**diagrams*, and introduce*Bregman*triangulations of a set of points and their connexion with*Bregman**Voronoi**diagrams*... Accordingly,*Bregman**Voronoi**diagrams*allow to define information-theoretic*Voronoi**diagrams*in statistical parametric spaces based on the relative entropy of distributions. ... First-type affine*Bregman**Voronoi**diagram*(red), second-type*Bregman**Voronoi**diagram*(blue) and symmetrized*Bregman**Voronoi**diagram*(green). 1. computing the first-type*Bregman**Voronoi**diagram*vorF (S) ...##
###
Geometry and clustering with metrics derived from separable Bregman divergences
[article]

2018
*
arXiv
*
pre-print

We investigate fixed rate quantization and its codebook

arXiv:1810.10770v1
fatcat:2esjghsk5rc2zlctppwjdkneza
*Voronoi**diagrams*, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respect to these ... Riemann-*Bregman*distances. ... Figure 3 : 3 Four types of*Voronoi**diagrams*induced by a*Bregman*generator: The leftsided*Bregman**Voronoi**diagram*(blue), the right-sided*Bregman**Voronoi**diagram*(red), the symmetrized*Bregman**Voronoi*...##
###
A Generic Statistics-Based Tessellation Method of Voronoi Diagram

2015
*
Journal of Systems Science and Information
*

AbstractIn terms of distance function and spatial continuity in

doi:10.1515/jssi-2015-0568
fatcat:bq34azz36vdfzc5aktbn2jn4vu
*Voronoi**diagram*, a generic generating method of*Voronoi**diagram*, named statistical*Voronoi**diagram*, is proposed in this paper based upon ... In the light of Mahalanobis distance, not only ordinary*Voronoi*and weighted*Voronoi*are implemented, but also the theory of*Voronoi**diagram*is improved further. ... weighted*Voronoi**diagrams*in raster [3, 4] ; centroidal*Voronoi*tessellations on applications and algorithms [5, 6] ;*Bregman**Voronoi**diagrams*with*Bregman*divergence [7] and the fast dynamic*Voronoi*...##
###
Further results on the hyperbolic Voronoi diagrams
[article]

2014
*
arXiv
*
pre-print

We investigate the hyperbolic

arXiv:1410.1036v1
fatcat:zcovdun6pnd6fbijdkffogpney
*Voronoi**diagram*in the hyperboloid model and show how it reduces to a Klein-type model using central projections. ... In Euclidean geometry, it is well-known that the k-order*Voronoi**diagram*in R^d can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential ... HVDs from lower envelopes The*Voronoi**diagram*of a set P = {p 1 , ..., p n } of n points in R d w.r.t. ...##
###
Optimal voronoi tessellations with hessian-based anisotropy

2016
*
ACM Transactions on Graphics
*

Our approach sharply contrasts with previous anisotropic versions of

doi:10.1145/2980179.2980245
fatcat:yygraqrx4rabxhfg3a4sycy5fi
*Voronoi**diagrams*as it employs first-type*Bregman**diagrams*, a generalization of power*diagrams*where sites are augmented with not only ... We thus refer to the resulting anisotropic polytopal meshes as Optimal*Voronoi*Tessellations. ...*Bregman**diagrams*. ...##
###
Power to the Points: Validating Data Memberships in Clusterings
[article]

2013
*
arXiv
*
pre-print

We also demonstrate useful

arXiv:1305.4757v1
fatcat:4hhjc43qjfcgpotdrdzt2d7bya
*visualizations*of these scores; these might prove useful within an interactive analytics framework. ... We hope to develop better*visualizations*to accompany this method. And more generally we plan on studying other unsupervised learning tasks where local validation is important. ... It has been shown [6] that the*Bregman**Voronoi**diagram*on a collection of sites s 1 , . . . , s k defined as V i = {p|D φ (p, s i ) ≤ D φ (p, s j )∀j = i} is a convex polyhedron just like in the case ...##
###
Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity
[article]

2008
*
arXiv
*
pre-print

Especially we introduce the concept of the

arXiv:0803.3109v2
fatcat:k3mtauzkt5gyde3hbim5scscwi
*Voronoi**diagram*and the smallest enclosing ball problem to the space of quantum states. ... [80] showed some properties of*Voronoi**diagram*with respect to*Bregman*divergence, which is generalization of Kullback-Leibler divergence. Using the*Voronoi**diagram*, Nielsen et al. ...*Voronoi**diagrams*are not only useful for such applications as numerical calculation and*visualization*, but also useful for theoretical interpre-tation of a geometric object. ...##
###
Power to the Points: Validating Data Memberships in Clusterings

2013
*
2013 IEEE 13th International Conference on Data Mining
*

It lends itself to easy

doi:10.1109/icdm.2013.147
dblp:conf/icdm/RamanV13
fatcat:5xge7b74k5botg5h4576mgawd4
*visualization*and can prove useful as part of an interactive*visual*analytics framework. ... We can also extend our*Voronoi*-based definition of affinity to clusterings in*Bregman*spaces [21] and kernel spaces [22] . ... Instead of constructing the*Voronoi**diagram*, we will construct the power*diagram*defined in Section III. ...##
###
An Obstruction to Delaunay Triangulations in Riemannian Manifolds

2017
*
Discrete & Computational Geometry
*

*Voronoi*

*diagrams*and Delaunay complexes can be defined for arbitrary Riemannian manifolds. ... The Delaunay complex of P is the nerve of the

*Voronoi*

*diagram*. ... Thus every

*Voronoi*face corresponds to a Delaunay simplex. The

*Voronoi*cells give a decomposition of M, denoted Vor M (P ), called the

*Voronoi*

*diagram*. ...

##
###
An obstruction to Delaunay triangulations in Riemannian manifolds
[article]

2016
*
arXiv
*
pre-print

*Voronoi*

*diagrams*and Delaunay complexes can be defined for arbitrary Riemannian manifolds. ... The Delaunay complex of P is the nerve of the

*Voronoi*

*diagram*. ... A schematic view of the

*Voronoi*

*diagram*associated with σ is depicted in Figure 3 . The circumumcentres of σ are the

*Voronoi*vertices shown in the

*diagram*. ...

##
###
Wavelet frame based surface reconstruction from unorganized points

2011
*
Journal of Computational Physics
*

Another popular technique is to construct a polyhedral surface from the input set of points utilizing the

doi:10.1016/j.jcp.2011.07.022
fatcat:se7iswshx5azjl2pkoalyt7ruu
*Voronoi**diagram*[2, 4, 3, 41, 23] , which is closely related to*Voronoi*-based algorithms for medial ... This leads to the alternative split*Bregman*algorithm for (3.2) . The derivation of splitting*Bregman*algorithm in [34, 8] is based on*Bregman*distance. It was recently shown (see e.g. ...
« Previous

*Showing results 1 — 15 out of 99 results*