A generalized solution of the orthogonal procrustes problem

By P. Schönemann, P. Schönemann. 1966

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

Word Translation Without Parallel Data (2017, methodology): “s jointly trained to fool the discriminator. Second, we extract a synthetic dictionary from the resulting shared embedding space and ﬁne-tune the mapping with the closed-form Procrustes solution from Schonemann (1966).¨ Since the method is unsupervised, cross-lingual data can not be used to select t”
A Survey of Cross-lingual Word Embedding Models (2017, methodology): “The complete regularizer then uses elastic net regularization to combine both terms: Ω = ∑ (sents,sentt)∈C α||ps − pt||2 + (1− α)‖ys − yt‖2 (49) The monolingual paragraph vector objectives LSGNS-P are then optimized jointly with the cross-lingual regularization term: J = LsSGNS-P(Ps,Xs) + LtSGNS-P(P”
Bias in word embeddings (2020, methodology): “The problem is solvable by applying a singular value decomposition algorithm as proposed by Schönman [86].”
A benchmarking study of embedding-based entity alignment for knowledge graphs (2020, unknown): “s (homepages of people and introductory images of products) and pre-trained word embeddings [87]. Besides, recent advances in unsupervised cross-lingual word alignment [11] like orthogonal Procrustes [64] and adversarial training [23] are also worth investigation. Another possible solution is to use”
Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel (2013, background): “This is referred to as the orthogonal Procrustes problem and [15] shows how the singular value decomposition gives the solution.”
Reconstructing 3D Human Pose from 2D Image Landmarks (2012, methodology): “We solve this as an instance of the Orthogonal Procrustes problem [28].”
Iterative Quantization: A Procrustean Approach to Learning Binary Codes for Large-Scale Image Retrieval (2013, unknown): “It has connections to the orthogonal Procrustes problem [41] and to eigenvector discretization for multiclass spectral partitioning [52], and in 2916 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 35, NO. 12, DECEMBER 2013 .”
Convex Optimization & Euclidean Distance Geometry (2004, background): “SOME ANALYTICAL OPTIMAL RESULTS maximizes Re tr(ASBR) : [215] [194] [36] [128] optimal orthogonal matrices S = UAU H B ∈ Rm×m , R = QBQ A ∈ Rn×n (1370) [sic] are not necessarily unique [134, §7.”
RESEARCH: "Consequences of a Multidimensional Approach to Religion for the Relationship Between Religiosity and Value Priorities" (2005, methodology): “Component scores were computed after orthogonal Procrustes rotation (McCrae, Zonderman, Costa, & Bond, 1996; Schonemann, 1966) of these components toward the average structure (see Figure 3) that was computed across 16 samples (Fontaine et al., 2003).”
Earth Mover’s Distance Minimization for Unsupervised Bilingual Lexicon Induction (2017, methodology): “…we choose the ground distance c to be the squared Euclidean distance L 22 , the program (10) is an extension of the orthogonal Procrustes problem (Sch¨onemann, 1966), which admits a closed-form solution: where U and V are obtained from a singular value decomposition (SVD): Note that the SVD is…”
COPA: Constrained PARAFAC2 for Sparse & Large Datasets (2018, unknown): “ows an Alternating Least Squares (ALS) approach to update the modes. First, orthogonal matrices {Qk }are solved by fixing H ,{Sk }, V and posing each Qk as an individual Orthogonal Procrustes Problem [22]: minimize {Qk} 1 2 ||Xk −QkH SkV T 2 F (2) Computingthesingularvaluedecomposition(SVD)ofH SkV T”
Guilford's Structure of Intellect Model and Model of Creativity: Contributions and Limitations (2001, methodology): “Yet, their interpretations of the data have been problematical as well, starting with those of Spearman, the inventor of factor analysis. Spearman (1904) claimed that his factor analyses supported the existence of a general factor and specific factors underlying his data.”
Meta‐Analysis of Dark Side Personality Characteristics and Critical Work Behaviors among Leaders across the Globe: Findings and Implications for Leadership Development and Executive Coaching (2015, methodology): “Moreover, to verify the structural equivalence of scales, global factors, and the overall assessment, Procrustes analyses (Schönemann, 1966) are used to find congruence coefficients between English and translated forms of the HDS.”