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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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Fitting the rotation between two sets of 3D points, given 1D measurements

Context: I am measuring a series of points on the surface of an object, with a measuring device which can only capture the position of a point perpendicular to the the surface being measured. I am ...
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How to compare different clusters of different size, rotation, scale and translation?

Assume that you have a matrix $X$ that contains the data inside the left image. The data inside $X$ is not classified. The matrix $X$ also contains outliers/noise. On the right, we can se the template ...
euraad's user avatar
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What is the size of Procrustes matrix?

Is there a contradiction in the presentations of orthogonal Procrustes rotation problem? In Matrix Computations by Golub&Van Loan (1) the orthogonal Procrustes problem is posed as an optimal ...
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procrustes alternative

Im comparing two multidimensional MDS solutions, the solutions have the same number of dimensions. I don't think I can use the permutation version of procrustes analysis (commonly, PROTEST in R::vegan)...
EAAndersson's user avatar
6 votes
1 answer
295 views

Procrustes Problem for rank-deficient input

It is well known that the solution to the orthogonal Procrustes problem $$ \textrm{arg min}_{\Omega \in \text{SO}(n)} ||Y - \Omega X||^2_2, $$ can be expressed in terms of an SVD of the covariance ...
const-ae's user avatar
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What is the difference between symmetric and non-symmetric in Procrustes/Protest analysis?

I'm basing my question off of someone else's stackoverflow post. My questions are the following: 1. A widely used R package vegan has a function called procrustes, ...
O.rka's user avatar
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What could be a good metric for rotation/translation-invariant image similarities?

An acquaintance posted an interesting image processing question. In the image below, we can tell that (a) and (c) are similar, whereas (b) is different. If we use (a) as a template and want to have a ...
Shan Dou's user avatar
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Determinant =1 constraint in PCA reconstruction Error

Let $q\leq p$. As in Tibshirani's statistical learning book, one can describe the PCA problem as optimizing the $q$-dimensional reconstruction error, given on a dataset $\{x_n\}_{n=1}^N$ in $\mathbb{...
ABIM's user avatar
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Implementing Procrustes rotation for factor scores, and least damaging alternatives

I am hoping to use multiple imputation to deal with missing continuous data (measured on a scale of 0-100) before conducting exploratory factor analysis (EFA), and to obtain factor scores for each ...
rumnraisin's user avatar
1 vote
1 answer
134 views

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 ...
phipsgabler's user avatar
5 votes
1 answer
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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 $\...
Adrian's user avatar
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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 ...
Antsushi's user avatar
5 votes
2 answers
714 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 $\...
amoeba's user avatar
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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 ...
Ben's user avatar
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4 votes
1 answer
180 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 ...
ttnphns's user avatar
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Comparing PCA solutions

I want to compare solutions provided by two instances of PCA, either due to two different implementations or due to two subsets of the data. One possible way is to calculate the similarity between ...
Krrr's user avatar
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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 ...
Julian Wittische's user avatar
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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 / ...
vphenix's user avatar
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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 ...
zlon's user avatar
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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 $U\in \mathbb{R}^{m\times d}$....
zunder's user avatar
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3 votes
1 answer
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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 ...
willnotburn's user avatar
3 votes
1 answer
737 views

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 ...
G. Herzlinger's user avatar
5 votes
2 answers
296 views

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 ...
Rob Goldstone's user avatar
4 votes
1 answer
288 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. ...
GoldFire's user avatar
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9 votes
2 answers
5k 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 ...
Wiliam's user avatar
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4 votes
1 answer
222 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 ...
Justine's user avatar
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3 votes
1 answer
1k 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 ...
aboSamoor's user avatar
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4 votes
2 answers
585 views

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 ...
Adb's user avatar
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2 votes
0 answers
437 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 ...
user2974849's user avatar
2 votes
0 answers
980 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 ...
user2364084's user avatar
6 votes
2 answers
2k 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 ...
Alberto acepsut's user avatar
7 votes
2 answers
3k views

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 ...
Peter Flom's user avatar
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5 votes
3 answers
9k views

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-...
dan's user avatar
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1 vote
1 answer
335 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 (...
Al-Ahmadgaid Asaad's user avatar
25 votes
5 answers
52k views

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 ...
Alex's user avatar
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1 vote
0 answers
1k views

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 ...
Simon's user avatar
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