A generalized solution of the orthogonal procrustes problem

Schönemann, Peter H.

doi:10.1007/bf02289451

Cited by 1,673 publications

(860 citation statements)

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“…Then, we made use of orthogo-506 nal Procrustes rotation to rotate these dimensions towards an 507 interpretable solution as this is considered a powerful tech-508 nique for conducting hypothesis-guided rotation (McCrae 509 et al 1996). Through this technique, dimensions are rotated 510 to minimize the sum of squares of deviations from a 511 hypothesized target matrix (Schönemann 1966). The rota-512 tion thus involves a realignment of the position of the axes, 513 without changing their relative position.…”

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confidence: 99%

The Jingle–Jangle Fallacy in Adolescent Autonomy in the Family: In Search of an Underlying Structure

Petegem

Vansteenkiste

Beyers

2012

J Youth Adolescence

124

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8 Abstract The construct of autonomy has a rich, though 9 quite controversial, history in adolescent psychology. The 10 present investigation aimed to clarify the meaning and 11 measurement of adolescent autonomy in the family. Based 12 on theory and previous research, we examined whether two 13 dimensions would underlie a wide range of autonomy-14 related measures, using data from two adolescent samples 15 (N = 707, 51 % girls, and N = 783, 59 % girls, age ran-16 ge = 14-21 years). Clear evidence was found for a two-17 dimensional structure, with the first dimension reflecting 18 ''volition versus pressure'', that is, the degree to which 19 adolescents experience a sense of volition and choice as 20 opposed to feelings of pressure and coercion in the parent-21 adolescent relationship. The second dimension reflected 22 ''distance versus proximity'', which involves the degree of 23 interpersonal distance in the parent-adolescent relationship. 24 Whereas volition related to higher well-being, less problem 25 behavior and a secure attachment style, distance was 26 associated mainly with more problem behavior and an 27 avoidant attachment style. These associations were not 28 moderated by age. The discussion focuses on the meaning 29 of adolescent autonomy and on the broader implications of 30 the current findings. 31 32

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confidence: 99%

The Jingle–Jangle Fallacy in Adolescent Autonomy in the Family: In Search of an Underlying Structure

Petegem

Vansteenkiste

Beyers

2012

J Youth Adolescence

124

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“…For instance, the nearest orthogonal matrix plays a role in computer vision [6], and we revisit its solution in Section 3. More or less equivalent to this is the solution to the orthogonal Procrustes problem [11]. For these and other matrix nearness problems we refer to [5,8].…”

Section: The Distance To a Matrix Groupmentioning

confidence: 99%

Euclidean distance degrees of real algebraic groups

Baaijens

Draisma

2015

Linear Algebra and its Applications

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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%

“…Eggert et al [10] reviewed the main methods that give an analytical solution to this rigid 3D registration problem: singular value decomposition (SVD) [9,19], unit quaternions [20], orthonormal matrix [21], and dual quaternions [22]. In [11], Gower and Dijksterhuis reviewed multiple different Procrustes problems and many generalizations.…”

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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A generalized solution of the orthogonal procrustes problem

Cited by 1,673 publications

References 8 publications

The Jingle–Jangle Fallacy in Adolescent Autonomy in the Family: In Search of an Underlying Structure

The Jingle–Jangle Fallacy in Adolescent Autonomy in the Family: In Search of an Underlying Structure

Euclidean distance degrees of real algebraic groups

Decomposition and dictionary learning for 3D trajectories

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