Introduction to 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.

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.

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.

To align two pose sequences, similar to [3], we apply Procrustes analysis to get a spatial transition matrix Q, which conducts an affine transformation, including translating, rotating and.

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.

The mantel test and procrustes analysis revealed that the gut microbial communities could be a key determinant for antibiotic and metal resistance.

The system uses a deep learning model for face mask detection and Procrustes analysis to measure the face identity similarity.

This is followed by localized Procrustes analysis to offset the affine transformation on temporary location values.

The coordinates configurations (x,y) were registered and aligned through Generalized Procrustes Analysis.

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).

Keywords: Geometric morphometry; Landmark; Morphological properties; 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.

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.

A generalized Procrustes analysis (GPA) was performed for shape analyses, filtering the effects of position, rotation, translation, and size.

Procrustes analysis and principal component analysis (PCA) were performed.

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).

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).

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

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).

Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation.

Finally, procrustes analysis showed the explanatory variables of the MGEs, the metabolites, and the microbial communities for the ARGs accounted for 94.

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.

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).

A novel haplotype-based approach that uses Procrustes analysis and automatic classification was used to provide further insights into tomato history and domestication.

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.

, 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.

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.

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.

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.

8 mm Procrustes analysis Mean Per Joint Position Error (P-MPJPE) in the Line of Sight (LoS) and Non-Line of Sight (NLoS) scenarios, respectively, achieving higher performance than the state-of-the-art method.

Procrustes analysis detected significant congruence between composition datasets.

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.

To separate size and shape information, 11 landmarks per wing were submitted to the Generalised Procrustes Analysis (GPA).

Two types of asymmetry – fluctuating and directional were evaluated in Procrustes analysis of variance.

rotation, projection and scaling) of each set based on a two-sided Wassertein Procrustes analysis (TWP).

The variables were analysed based on Generalized Procrustes analysis.

The congruence between the different taxonomic levels was evaluated using a Procrustes analysis.

Landmark coordinate data obtained and Procrustes analysis was used to compare mean shapes.

Procrustes analysis and principal component analysis (PCA) were performed.

Generalised Procrustes analysis showed the morphological characteristics of the superior proximal femur according to native anteversion amount.

The application of asymmetry analysis and Procrustes analysis in the evaluation of different crop rotations are given in details.

Procrustes analysis showed a significant relationship between the microbiome and metabolome datasets.

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.

Generalized Procrustes analysis could effectively exclude the influence of leaf position and size on leaf shape.

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.

Procrustes analysis showed a significant relationship between the microbiome and metabolome datasets.

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.

In this study, the Generalized Procrustes Analysis was proposed as a basis for obtaining a factorial plane where all individuals are projected.

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).

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.

In this paper, we proposed a two-stage CP algorithm that combines multidimensional scaling (MDS) and Procrustes analysis for vehicles with GPS information.

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

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.

To analyze how different components of leaf morphology vary across lineages, we employed Procrustes Analysis of Variance (ANOVA), two-block partial least-square analysis (2B-PLS), and several other multivariate analysis approaches.

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

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.

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.

ARG and microbiota compositions were correlated (Procrustes analysis, p=0.

The first two dimensions of the Generalized Procrustes Analysis represent 83.

We highlight three technical innovations: full batch learning via relational matrices, closed-form Orthogonal Procrustes Analysis for KGEs, and non-negative-sampling training.

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.

Vertebral body length (VBL) was measured to calculate the proportions of each tail region and to perform procrustes analysis on the shape of relative vertebral body length (rVBL) progressions.

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.

There was significant inter-omic concordance based on Procrustes analysis (6 weeks: p  = 0.

The Generalized Procrustes Analysis was provided and the difference in the variance of paired landmarks was indicated.

The findings are visualised with a repertory grid software using Generalised Procrustes Analysis (GPA).

Then Procrustes analysis is applied to accelerate the program as a coarse-to-fine strategy.

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.

The evaluation, involving Multidimensional Scaling, Generalized Procrustes Analysis as well as Internal and External Preference Mapping, identified two separate perceptual dimensions.

Acetabular shape and the position of the centre of the acetabular component were analyzed by morphometric geometrical analysis using the generalized Procrustes analysis.

Facial landmarks were digitized and the corresponding coordinates were submitted for Generalized Procrustes Analysis.

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.

The obtained landmark configurations were superimposed by the General Procrustes Analysis to remove non-shape variations.

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.

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.

Procrustes analysis suggested that microbial community composition was the determining factor of the ARG profile but not for MRG.

Procrustes analysis and principal component analysis (PCA) were performed.

The terms Procrustes Analysis and Procrustes Techniques are referred to a set of least squares mathematical models used to perform transformations among corresponding points belonging to a generic k-dimensional space, in order to satisfy their maximum agreement.

Procrustes analysis and the Mantel test both indicate that soil bacterial communities were significantly correlated with ARG profiles.

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.

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.

Shape variables were computed as principal components of the “partial warp” calculated after generalized procrustes analysis of raw coordinates.

As extensively shown in the previous chapters, Procrustes Analysis allows to easily perform transformations among corresponding point coordinates belonging to a generic k-dimensional space and it is therefore suited to solve problems encountered in geodesy, photogrammetric computer vision, and laser scanning.

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.

Shape variables were used to estimate wing shape and were calculated from the Generalized Procrustes Analysis following principal components of the partial warp.

A Generalized Procrustes Analysis was used to standardize size differences and reveal shape differences.

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.

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.

The Generalized Procrustes analysis was used to obtain mean shapes of the preoperative and postoperative term.

During wing shape analysis, shape variables were analyzed from principal components of partial warp scores calculated after generalized procrustes analysis of coordinates.