Procrustes Problems

By Marco F. R Amoni. 2005

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Citations in the corpus

Accelerating Very Deep Convolutional Networks for Classification and Detection (2015, background): “(6) Here {zi} is a set of auxiliary variables of the same size as {yi}. λ is a penalty parameter.”
Efficient and accurate approximations of nonlinear convolutional networks (2014, methodology): “The GSVD is applied on M̂ as M̂ = USV>, such that U is a d-by-d orthogonal matrix satisfying U>U = Id where Id is a d-by-d identity matrix, and V is a d-by-d matrix satisfying V>YY>V = Id (called generalized orthogonality).”
Visualizing the Hidden Activity of Artificial Neural Networks (2017, unknown): “The (arguably) simplest way to do this is to compute Ap[t] independently for each t, and use point-cloud registration [13] to align the resulting projections.”
A modified sorting task to investigate consumer perceptions of extra virgin olive oils (2010, methodology): “An example of such a statistical technique is generalized Procrustes analysis (GPA), which finds a compromise matrix iteratively from a set of factor score matrices (Gower & Dijksterhuis, 2004; Meyners, 2003; Meyners, Kunert, & Qanari, 2000).”
A Local/Global Approach to Mesh Parameterization (2008, methodology): “In other words: This problem can be solved using Procrustes analysis [GD04], and its solution in general is computed using the Singular Value Decomposition (SVD) of J .”
missMDA: A Package for Handling Missing Values in Multivariate Data Analysis (2016, unknown): “Individuals (using their scores) are represented in the same subspace with Procrustes rotations (Gower and Dijksterhuis 2004).”
TEASER: Fast and Certifiable Point Cloud Registration (2020, unknown): “The Wahba problem is also related to the well-known Orthogonal Procrustes problem [46] where one searches for orthogonal matrices (rather than rotations), for which a closed-form solution also exists [47].”
Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems (2016, result): “The equality is established only when where F H opt F RF = UΣV H = USV H 1 , which is the SVD of F H opt F RF , and S is a diagonal matrix whose elements are the ﬁrst N s nonzero singular values σ 1 , · · · , σ N s . the This result bears some similarity to the solution of orthogonal Procrustes prob”
Sparse projections for high-dimensional binary codes (2015, background): “On the contrary, the procrustes solution [12] is not valid when b < d.”
Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame (2011, methodology): “The well known results for the orthogonal Procrustes problem [14] are adopted to determine VL ∈ O(3).”
Multiple factor analysis: principal component analysis for multitable and multiblock data sets (2013, background): “In GCCA, 137–139 the goal is to maximize the inner-product of the factor scores of the compromise under a constraint that makes it equivalent to maximizing the correlations between the compromise factor scores and the partial factor scores.”