Questions tagged [procrustes-analysis]

A form of shape analysis where one set of points is rotated in some way to try to superimpose it over another set of points to achieve maximal overlay fit.

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How can this L(2,1) problem be reduced to the orthogonal procrustes problem?

NOTE: Don't take this too serious -- the question is actually due to my misreading $\|y_i - Wx_i\|^2$ as $\|y_i - Wx_i\|_2$, see the answer. Smith et al. in Offline bilingual word vectors, orthogonal ...
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Procrustes Analysis: Interpreting an Impulse Diagram of Residuals

I have applied 3 MDS techniques to a data set. They are; classical metric scaling, Kruskal's non-metric scaling and Sammon's metric least squares scaling. In order to compare the 3 configurations I am ...
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105 views

Derivation of Procrustes transformation

I'm curious about the derivation for the Procrustes transformation. I'm following ESLII: see figure 14.25 and problem 14.8 (Procrustes distance with scaling). Given matrices $\mathbf{X}_1$ and $\...
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Procrustes superimposition and sliding in integrated structures

Assume I have the following structure. Black dots represent semilandmarks to be slid, and red dots are "anatomical", or "fixed", landmarks. They are both dependent on each other, so that the ...
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2answers
293 views

Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix

Let $\mathbf A$ be an arbitrary $n \times m$ matrix with $n \ge m$. I want to find $\mathbf X$ of the same size with orthonormal columns that minimizes the Frobenius norm of the difference between $\...
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184 views

How to match curves or measure the similarity between both?

Firstly, I'm not sure whether this is the correct site but I also assume the question is not too different: Assume there are two curves: One is considered as a reference curve and the other is just ...
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82 views

Ways to modify data minimally while the variables to follow the desired covariances

Let $\bf X$ be the p-variate dataset. I want to modify the data to p-variate data $\bf Y$ so that its variables satisfy ...
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216 views

Residuals of symmetric Procrustes analyses are not symmetric

I am trying to replicate the analysis I saw in a paper. One of the step is to describe the relationships between two data tables. I use the procrustes() function ...
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Does RMSD-based estimation conserve the estimated data distribution?

Let's say I have two sets of paired points $\{x_i\}_{i=1..n}$, $\{y_i\}_{i=1..n}$ defined in an $N$-dimensional space and I want to use the Kabsch algorithm to estimate the best rotation matrix / ...
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79 views

How to prove that new data fits old PCA

I have an old dataset, for which i perform PCA, show its significance (non-randomness). Now I have new data (obtained in a bit different conditions). And I want to say that independently from ...
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Learning samples from similarity matrix

Having a set of points $X\in\mathbb{R}^{n\times d}$ and a similarity matrix $S\in \mathbb{R}^{n\times m}$, I am interested in an approximation of the second set of points $U\in \mathbb{R}^{m\times d}$....
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NMDS from Jaccard and Bray-Curtis identical. Is that a bad thing?

The dataset is ecological (species abundance), where I am calculating distances between 51 sampling sites, based on abundances of 3200 species. The species abundance values go up to 2700, and the rest ...
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how to calculate observation within and between groups variances of PCA scores

I'm kind of new here, and also not a professional statistics guy, so sorry if the answer is obvious and I'm missing something, but I looked everywhere and couldn't figure it out. I'm doing geometric ...
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Finding optimal correspondences between objects given two square distance matrices

I would like to find the optimal correspondences between two systems of objects based on the distances between objects WITHIN the two systems. So, the input to the algorithm would be two square ...
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215 views

Multivariate Analysis of Ecological Data: Procrustes analyses or GLM?

I have a dataset containing 6 variables (vegetation cover in percent) and the number of species found in 30 areas. I would like to test if the different vegetation covers explain species richness. ...
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854 views

Find the rotation between set of points

I have two sets (sourc and target) of points (x,y) that I would like to align. What I did so ...
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1answer
123 views

Compare Procrustes values

I have two sets of spatial data which underwent a transformation. I'd like to compare the effect of the transformation on two sets of data to test the hypothesis that the transformation had a larger ...
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412 views

Multiple linear regression through orthogonal matrices

An example of linear regression could look like: $min \sum_{i=0}^{m}||x_i A - y_i||_2^{2}$, where ${x_i, y_i} \in \mathbb{R}^n$ and $A \in \mathbb{R}^{n\times n}$. I am interested in knowing how do ...
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Is factor analysis appropriate for repertory grid data?

I've used factor analysis for questionnaires and such before, but I have a new research question now and it doesn't seem like anything similar has been done. I've had participants rate 8 news articles ...
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370 views

Comparing facial curvature of two human faces

I need help determining if what I'm doing is sufficient. I have extracted the "curvature" from two human faces (essentially the curve that goes from one ear, down the face to the chin, and back up to ...
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792 views

Procrustes Analysis of 3d point cloud without defined landmarks

I am working with several hundred 3d point clouds generated using a 3d scanner and would like to be able to compare their shapes using something like a procrustes analysis. Instead of manually ...
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993 views

Looking for a test for shape comparison

I have two different time series both length = 100 and I need to know what is the best test (non-parametric, if possible), that return how much these two series are same or similar shapes. Here are ...
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Factor analysis on multiply imputed data

I have a data set with approximately 500 observations on eight key variables. There are a lot of missing data; only about 1/12 of the observations are complete. I am using ...
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How to reduce the number of variables in cluster analysis?

I've got 10 (yes, only 10) cases over 1000 variables (e.g. measurements of concentrations of 1000 different compounds at 10 different time points). I can group these cases into 3 clusters in 1000-...
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1answer
274 views

Methods of “Two-Way” Multidimensional Scaling (MDS)?

I just want to ask about the MDS. Below is the subcategory of the Multidimensional Scaling topic. Multidimensional Scaling Metric and Non-Metric Models Methods of "Two-Way" Multidimensional Scaling (...
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Similarity measures between curves?

I would like to compute the measure of similarity between two ordered sets of points---the ones under User compared with the ones under Teacher: The points are curves in 3D space, but I was thinking ...
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Template matching involving scale-, rotation- and shape-invariant transformation

I am not sure whether this is the right place to ask this question, but any possible answer will help. I want to apply some form of template matching on these set of pictures. This is the template ...