Procrustes Problems

Gower, J. C.; Dijksterhuis, Garmt

doi:10.1093/acprof:oso/9780198510581.001.0001

Cited by 675 publications

(509 citation statements)

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“…In addition, we are considering various future improvements. For instance, we can make use of Procrustes analysis [45] as proposed by Garcia-Fernandez et al [46] to align basic projections avoiding the use of control points. The use of multi-objective metrics combined with optimization strategies is also an aspect we are currently investigating, which should impact positively the overall user experience.…”

Section: Discussion and Limitationsmentioning

confidence: 99%

Projection inspector: Assessment and synthesis of multidimensional projections

et al. 2015

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Section: Discussion and Limitationsmentioning

confidence: 99%

Projection inspector: Assessment and synthesis of multidimensional projections

et al. 2015

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“…This problem has not been addressed, and we ignore if an analytic solution exists to solve it. It can be viewed as a generalization of the orthogonal Procrustes problem [9,10,11,12], which usually deals with the registration of a single pattern. In our study, the shift-invariant case will be considered hereafter.…”

Section: The Organizationmentioning

confidence: 99%

“…In [11], Gower and Dijksterhuis reviewed multiple different Procrustes problems and many generalizations. However, they did not address our problem in Eq.…”

Section: Rigid 3d Registration or Orthogonal Procrustes Problemmentioning

confidence: 99%

Decomposition and dictionary learning for 3D trajectories

2014

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A new model for describing a three-dimensional (3D) trajectory is proposed in this article. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This article is divided into two parts based on this model. On the one hand, the 3DRI decomposition estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language.

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“…Solving this is a known problem in Procrustes analysis [1,11] and the solution (the Procrustes statistic) is…”

Section: Ep |mentioning

confidence: 99%

Efficient Node Overlap Removal Using a Proximity Stress Model

Gansner

2009

Graph Drawing

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Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a post-processing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using little additional area. This paper presents a new node overlap removal algorithm that does well by these measures.

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Procrustes Problems

Cited by 675 publications

References 0 publications

Projection inspector: Assessment and synthesis of multidimensional projections

Projection inspector: Assessment and synthesis of multidimensional projections

Decomposition and dictionary learning for 3D trajectories

Efficient Node Overlap Removal Using a Proximity Stress Model

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