## What is/are Procrustes Analysis?

Procrustes Analysis - This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized canonical correlation analysis (CCA), Procrustes analysis, and cryo-electron microscopy of the Nobel prize fame.^{[1]}The system uses a deep learning model for face mask detection and Procrustes analysis to measure the face identity similarity.

^{[2]}This study explores various IVS methods, including Gamma test (GT), Procrustes analysis (PA) and Edgeworth approximation-based conditional mutual information (EA) and evaluates their ability to improve Rs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{s}$$\end{document} prediction accuracy by coupling them with popular non-linear data-driven models, multilayer perceptron (MLP), support vector machine, extreme learning machine and multi-gene genetic programming (MGGP).

^{[3]}Keywords: Geometric morphometry; Landmark; Morphological properties; Procrustes analysis.

^{[4]}Then, using the pooled data, we calculated non-metric multidimensional scaling ordinations (NMDS) from all types of dissimilarity matrices and made pairwise comparisons using Procrustes analysis.

^{[5]}Procrustes analysis and principal component analysis (PCA) were performed.

^{[6]}Applied on four different image datasets, which include scarab beetle genitalia (Pleophylla, Schizonycha) as well as wing patterns of bees (Osmia) and cattleheart butterflies (Parides), our augmentation approach outperformed a deep learning baseline approach by means of resulting identification accuracy with non-augmented data as well as a traditional 2D morphometric approach (Procrustes analysis of scarab beetle genitalia).

^{[7]}The proposed solution uses a nonlinear complimentary ﬁlter for self-pose estimation using only an IMU, a particle ﬁlter for relative pose estimation between UAS using a relative range measurement, visual target tracking using a gimballed camera when the target is close to the handoff UAS, and track correlation logic using Procrustes analysis to perform the ﬁnal target handoff between vehicles.

^{[8]}Structural equation model analysis showed that the soybean growth period affected the composition of ARGs by affecting the microbial community, which was further supported by Procrustes analysis (P < 0.

^{[9]}, the biophysical composition index calculated using the Gram–Schmidt orthogonalization method, biophysical composition index calculated using a principal component-based Procrustes analysis, Normalized Built-up Area Index (NBAI), combinational build-up index, and perpendicular impervious surface index (PISI)) and three impervious surface binary methods (i.

^{[10]}For the second objective, we used Procrustes analysis to assess the shape variation of these two anatomical regions, the bivariate plots of Principal Components to evaluate their shape space, and a two‐block Partial Least Square (PLS) to explore their covariation.

^{[11]}The geometric morphometric data were based on the fourteen landmarks of each internal valve, performed by TPSDig, and the morphometric and statistical analyses, carried out with MorphoJ, were Procrustes analysis, Procrustes Anova, principal components analysis, discriminant function analysis, and regression analysis.

^{[12]}We used linear models, redundancy analysis, Procrustes analysis and Holm-corrected multiple t-tests to quantify the effects of the plot-level tree neighborhood on the diversity and composition of foliar fungal endophytes in Fagus sylvatica, Quercus petraea and Picea abies.

^{[13]}Two types of asymmetry – fluctuating and directional were evaluated in Procrustes analysis of variance.

^{[14]}The congruence between the different taxonomic levels was evaluated using a Procrustes analysis.

^{[15]}Landmark coordinate data obtained and Procrustes analysis was used to compare mean shapes.

^{[16]}Procrustes analysis and principal component analysis (PCA) were performed.

^{[17]}The application of asymmetry analysis and Procrustes analysis in the evaluation of different crop rotations are given in details.

^{[18]}We show that our approach can benefit from, but does not require, post-processing steps such as Procrustes analysis, in contrast to some of our baselines which require it for reasonable performance.

^{[19]}We assessed the distribution and abundance of epiphytic moss and tree species separately by performing an ordination analysis for each plot and tested if the spatial pattern of mosses was correlated with that of trees by performing a Procrustes analysis.

^{[20]}Procrustes analysis was used to quantify the resemblance between pairs of PCA ordinations based on soil properties (d) and various biotic communities (a, b, c).

^{[21]}Procrustes analysis of variance (Procrustes ANOVA) indicated that variation of leaf blade shape was weakly associated with geography and was mainly explained by taxa themselves.

^{[22]}The semantic transformation between the shape template and the current curve is obtained by Procrustes analysis and then adopted to update the current curve to resemble the shape prior.

^{[23]}Procrustes analysis and principal component analysis (PCA) were performed.

^{[24]}Procrustes analysis and the Mantel test both indicate that soil bacterial communities were significantly correlated with ARG profiles.

^{[25]}In this work, we propose a calibration method using Procrustes analysis in combination with an outlier correction algorithm, which is based on a model of the calibration data and on the geometry of the experimental setup.

^{[26]}Procrustes analysis and redundancy analysis demonstrated that shifts in the bacterial community determined the changes in the abundances of ARGs, and the variation in MGEs and DTPA-Cu can also partially explain the ARG variance.

^{[27]}The framework is based on the integration of multidimensional scaling (MDS) and Procrustes analysis (PA) multivariate techniques.

^{[28]}As diffusion maps could not get explicit map, Procrustes analysis is applied to facilitate the on-line monitoring.

^{[29]}In this paper, after aligning the poses obtained from single images using Procrustes Analysis, median filtering is utilized to eliminate outliers to find final reconstructed 3D body joint coordinates.

^{[30]}Aiming at the problem of continuous model updating for fault recognition in the time-varying process, a novel method called the Procrustes analysis–based Fisher discriminant analysis was proposed.

^{[31]}that consists of two main components: Dynamic Time Warping (DTW) and Procrustes analysis (PA).

^{[32]}The intramuscular portion of arteries, veins, and nerves was dissected, traced on transparencies, and digitized before adjustment to an average muscle shape using Procrustes analysis to generate density distributions for the relative positions of these structures.

^{[33]}Procrustes analysis was used and principal component analysis was performed to reveal the main patterns of palatal shape variation.

^{[34]}Method: We propose a method based on Procrustes analysis for matching the statistical distributions of two datasets using simple geometrical transformations (translation, scaling, and rotation) over the data points.

^{[35]}In this paper, we propose a registration method using Correlation Coefficients of the point cloud dimensions along with pose calculated by Procrustes Analysis to provide an ideal global registration for the Iterative Closest Point (ICP) algorithm.

^{[36]}We then aligned the shapes using Procrustes analysis, before proceeding to reduce the dimensionality using PCA.

^{[37]}To assess the ability of different taxa to serve as surrogates for others, we carried out a Procrustes analysis on the beta diversity patterns of seven biological groups (aquatic birds, Amphibians, Macrophytes, Coleoptera, Odonata, Heteroptera and phytoplankton) in 35 ponds of the Cerrado biome.

^{[38]}Procrustes Analysis (PA) is commonly used to find the optimal orthogonal word mapping in the bilingual case.

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## Generalized Procrustes Analysis

We project all the models to a shared vector space using an efficient implementation of the Generalized Procrustes Analysis (GPA) procedure, previously used in multilingual word translation.^{[1]}The coordinates configurations (x,y) were registered and aligned through Generalized Procrustes Analysis.

^{[2]}A generalized Procrustes analysis (GPA) was performed for shape analyses, filtering the effects of position, rotation, translation, and size.

^{[3]}Our results indicated that all sensory attributes of the attribute map were affected (generalized procrustes analysis (GPA) explained 100% of the total variability among treatments).

^{[4]}We analyzed the difference in the shapes of T-waves between LQTS3 cases and normal subjects using generalized Procrustes analysis (GPA).

^{[5]}From the study, the RPM method was able to highlight an area of innovation where two of the 3-blend prototypes were loaded together with the commercial plant-based milk alternative in the 2D consensus map generated from Generalized Procrustes Analysis (GPA).

^{[6]}Using multidimensional ordination and generalized Procrustes analysis, the dynamics of the distribution of ecosystem objects (individual species and areas) in the coordinates of two latent axes of maximum variation is shown.

^{[7]}The variables were analysed based on Generalized Procrustes analysis.

^{[8]}Generalized Procrustes analysis could effectively exclude the influence of leaf position and size on leaf shape.

^{[9]}In this study, the Generalized Procrustes Analysis was proposed as a basis for obtaining a factorial plane where all individuals are projected.

^{[10]}Having established the correspondence, we computed the mean shape using full generalized Procrustes analysis and constructed an SSM by means of principal component analysis.

^{[11]}Here, geometric morphometric data from 19 homologous landmarks on the left wing of males from seven species of Calliphoridae (n = 55), and eight species of Sarcophagidae (n = 40) were obtained and processed using Generalized Procrustes Analysis.

^{[12]}Therefore, the purpose of this work is to compare the COSTATIS method and generalized Procrustes analysis (GPA) when working with multi-way data.

^{[13]}We analyzed the difference in the shapes of the T-waves of V5 in the electrocardiograms (ECGs) of LQTS3 cases and normal subjects using generalized Procrustes analysis.

^{[14]}The first two dimensions of the Generalized Procrustes Analysis represent 83.

^{[15]}Generalized Procrustes Analysis revealed that a general consensus between participants for dromedary behavioural features were reached, more substantial for those expressions reflecting agitation and/or indifference towards interaction with human.

^{[16]}The Generalized Procrustes Analysis was provided and the difference in the variance of paired landmarks was indicated.

^{[17]}Ontogenetic changes in corpus growth from the eruption of M1 to the eruption of M3 were evaluated for each species through generalized Procrustes analysis and principal components analysis in shape-space and form-space.

^{[18]}The evaluation, involving Multidimensional Scaling, Generalized Procrustes Analysis as well as Internal and External Preference Mapping, identified two separate perceptual dimensions.

^{[19]}Acetabular shape and the position of the centre of the acetabular component were analyzed by morphometric geometrical analysis using the generalized Procrustes analysis.

^{[20]}Facial landmarks were digitized and the corresponding coordinates were submitted for Generalized Procrustes Analysis.

^{[21]}Therefore, to address such a fundamental issue that poses a stiff challenge to the recognition procedure we, in this paper, propose an algorithm for recognition which is based on Anisotropic Generalized Procrustes Analysis (AGPA) of the similarity between the test PDVP image and the weighted training samples.

^{[22]}The diagrams, constructed and analyzed with the use of the cluster and Generalized Procrustes analysis, enable us to isolate stable associations of taxa typical for particular biotopes with homogeneous environmental conditions.

^{[23]}Shape variables were computed as principal components of the “partial warp” calculated after generalized procrustes analysis of raw coordinates.

^{[24]}Shape variables were used to estimate wing shape and were calculated from the Generalized Procrustes Analysis following principal components of the partial warp.

^{[25]}A Generalized Procrustes Analysis was used to standardize size differences and reveal shape differences.

^{[26]}Wing-shape variables were computed as Procrustes superimposition with residual coordinates of the 18 landmarks following a Generalized Procrustes Analysis and the principal components of residual coordinates.

^{[27]}MATERIALS AND METHODS Outlines of the mandibular corpus in cross-section between M1 and M2 were quantified in a sample of hominoids and analyzed using generalized Procrustes analysis, Procrustes ANOVA, CVA, and cluster analysis.

^{[28]}The Generalized Procrustes analysis was used to obtain mean shapes of the preoperative and postoperative term.

^{[29]}During wing shape analysis, shape variables were analyzed from principal components of partial warp scores calculated after generalized procrustes analysis of coordinates.

^{[30]}The morphology of the inner and outer cortices of the mandible was analyzed using statistical shape analysis, including generalized Procrustes analysis and principal component analysis (PCA).

^{[31]}Additionally, for each of the four pubertal‐staged age cohorts, sex‐specific vertebral body wireframes were superimposed using generalized Procrustes analysis to determine sex‐specific changes in form (size and shape) and shape alone.

^{[32]}15 To analyze the 2D or 3D morphology, several studies have used the Generalized Procrustes Analysis (GPA),16,17 which is a method of morphometric geometrical analysis.

^{[33]}Generalized Procrustes Analysis (GPA) is a multivariate statistic method that is used at the evaluation of sensory analyses in the food industry.

^{[34]}The generalized Procrustes analysis is used to estimate a standard normal mean gait shape (NMGS) for ten young subjects.

^{[35]}Size and shape variation in the pelvis and soft tissue morphology was characterized using the Generalized Procrustes Analysis to compute the mean configuration.

^{[36]}Shape difference was assessed by performing Generalized Procrustes analysis.

^{[37]}3D scanning model of the maxilla was analysed by Generalized procrustes analysis (GPA) and principal component analysis (PCA).

^{[38]}Finally, an improved random sample consensus (RANSAC) generalized Procrustes analysis (RGPA) method was employed to register and optimize the partial models into a complete indoor scene.

^{[39]}Twenty-three two-dimensional anatomical landmarks were digitized on the mandible and superimposed using generalized Procrustes analysis, which projects landmarks into a common shape space.

^{[40]}Landmark sets were superimposed using generalized Procrustes analysis prior to statistical analysis.

^{[41]}Generalized Procrustes Analysis (GPA) demonstrated the consensus between soil, water, forage and milk, in addition to differences between studied areas.

^{[42]}We digitized 19 cranial landmarks and conducted generalized Procrustes analysis, principal component analysis (PCA), principal component analysis between groups (bg‐PCA), and a branch weighted squared‐change parsimony approach.

^{[43]}For head shape, landmarks were analyzed by generalized procrustes analysis, principal component analysis (PCA), Mahalanobis distance, discriminant function analysis, cross-validation and unweighted pair-group method clustering (UPGMA).

^{[44]}QBA scores were analysed using Generalized Procrustes Analysis.

^{[45]}We paired an analysis of finite trait attributes with a 17-point landmark survey and generalized Procrustes analysis (GPA) to reconstruct grapevine leaves digitally from five interspecific hybrid mapping families.

^{[46]}Then, the Generalized Procrustes analysis (GPA) method is employed to normalize the extracted features.

^{[47]}We carried out Generalized Procrustes Analysis, Principal Components, and Regression analyses to evaluate shape variation; and complemented these analyses with the Cobb Method.

^{[48]}RESULTS Results from generalized procrustes analysis (GPA) showed that panel performance by QDA was more repeatable and reached higher homogeneity than that by FP.

^{[49]}The data was processed by using generalized procrustes analysis.

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## General Procrustes Analysis

A set of statistical tools including Multidimensional Scaling, Correspondence Analysis, Individual Difference Scaling, and General Procrustes Analysis was applied to discriminate among sample groups with the purpose to reveal meaningful compositional patterns and infer sediment transport pathways on a geological scale.^{[1]}After using general procrustes analysis (GPA) to align the sets of 63 skulls with coronary craniosynostosis represented by 209 landmarks, discrete cosine transform (DCT) is utilized to approximate five kinds of bones of facial cranium curves, including 43 affected patients and 20 normal persons.

^{[2]}A set of statistical tools including Multidimensional Scaling, Correspondence Analysis, Individual Difference Scaling, and General Procrustes Analysis was applied to discriminate among sample groups with the purpose to reveal meaningful compositional patterns and infer sediment transport pathways on a geological scale.

^{[3]}Background This study is aimed to (1) investigate the influence of sagittal and vertical patterns on mandibular cross-sectional morphology and to (2) provide visualized mandibular cross-sectional morphology in different groups with General Procrustes Analysis (GPA), canonical variance analysis (CVA) and discriminant function analysis (DFA).

^{[4]}A general Procrustes analysis identified two main descriptive dimensions of elephant behavioral expression explaining 27% and 19% of the variability in the children group, 19% and 23.

^{[5]}The other three examples of suture curves abstracted from 3D human skulls on which semilandmarks and landmarks are aligned with General Procrustes Analysis (GPA) to eliminate the effect brought by location, size, and orientation.

^{[6]}General Procrustes analysis revealed significantly smaller molars and dimensions of the alveolar bone in the mandible of the miR-21 knockout mice when compared with wild-type controls (P=0.

^{[7]}The obtained landmark configurations were superimposed by the General Procrustes Analysis to remove non-shape variations.

^{[8]}Pattern of shape variation along the axes of the principal components and canonical variates were analyzed after the General Procrustes analysis.

^{[9]}SCR extracts clusters by a sequentially partitioning obtained by combining fuzzy clustering techniques and general Procrustes analysis.

^{[10]}Analyzing FCP data with a General Procrustes Analysis, varieties were separated in different factors for flavor and texture, but not appearance.

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## Generalised Procrustes Analysis

To separate size and shape information, 11 landmarks per wing were submitted to the Generalised Procrustes Analysis (GPA).^{[1]}Generalised Procrustes analysis showed the morphological characteristics of the superior proximal femur according to native anteversion amount.

^{[2]}The findings are visualised with a repertory grid software using Generalised Procrustes Analysis (GPA).

^{[3]}Generalised Procrustes Analysis was used to test the differences found by panellists.

^{[4]}The generalised Procrustes analysis was used to obtain mean shapes in the pre- and postoperative phases.

^{[5]}This chapter presents a review of commonly used methods for digital acquisition, extraction and landmarking of anatomical structures and of the common geometric morphometric statistical methods applied to investigate them: generalised Procrustes analysis to derive shape variables, principal component analysis to examine patterns of variation, multivariate regression to examine how form is influenced by meaningful factors and partial least squares analysis to examine associations among structures or between these and other interesting variables.

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## procrustes analysis showed

Finally, procrustes analysis showed the explanatory variables of the MGEs, the metabolites, and the microbial communities for the ARGs accounted for 94.^{[1]}Generalised Procrustes analysis showed the morphological characteristics of the superior proximal femur according to native anteversion amount.

^{[2]}Procrustes analysis showed a significant relationship between the microbiome and metabolome datasets.

^{[3]}Procrustes analysis showed a significant relationship between the microbiome and metabolome datasets.

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## procrustes analysis revealed

The mantel test and procrustes analysis revealed that the gut microbial communities could be a key determinant for antibiotic and metal resistance.^{[1]}General Procrustes analysis revealed significantly smaller molars and dimensions of the alveolar bone in the mandible of the miR-21 knockout mice when compared with wild-type controls (P=0.

^{[2]}Generalized Procrustes Analysis revealed that a general consensus between participants for dromedary behavioural features were reached, more substantial for those expressions reflecting agitation and/or indifference towards interaction with human.

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## procrustes analysis indicated

The results of the Mantel test and Procrustes analysis indicated that ARG profiles in soil were significantly correlated with the structure of the bacterial phylogeny.^{[1]}Morphometry and Procrustes analysis indicated that changes in the femur shape after ossification were limited, which were mainly detected at the time of initial ossification and shortly after that.

^{[2]}