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.
34
questions
0
votes
0
answers
29
views
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)...
5
votes
1
answer
202
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 ...
- 247
0
votes
0
answers
69
views
Procrustes rotation when computing confidence intervals for PCA weights
I would like to compute confidence intervals for my feature weights derived from a PCA using a resampling procedure. I found a lot of different threads that deal with two major issues here when doing ...
- 161
2
votes
1
answer
245
views
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, ...
- 1,422
2
votes
0
answers
317
views
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 ...
- 455
1
vote
2
answers
118
views
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{...
- 544
1
vote
0
answers
149
views
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 ...
- 53
1
vote
1
answer
128
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 ...
- 95
5
votes
1
answer
444
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 $\...
- 4,212
2
votes
0
answers
50
views
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 ...
- 21
5
votes
2
answers
661
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 $\...
- 101k
2
votes
1
answer
1k
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 ...
- 3,123
4
votes
1
answer
172
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 ...
- 56k
1
vote
0
answers
793
views
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 ...
- 500
1
vote
0
answers
322
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 ...
- 175
1
vote
0
answers
20
views
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 / ...
- 517
0
votes
0
answers
193
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 ...
- 718
1
vote
0
answers
79
views
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 $U\in \mathbb{R}^{m\times d}$....
- 161
3
votes
1
answer
4k
views
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 ...
- 61
3
votes
1
answer
691
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 ...
5
votes
2
answers
293
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 ...
4
votes
1
answer
279
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.
...
- 141
8
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 ...
- 223
4
votes
1
answer
203
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 ...
- 41
3
votes
1
answer
924
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 ...
- 133
4
votes
2
answers
576
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 ...
- 41
2
votes
0
answers
435
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 ...
- 293
2
votes
0
answers
956
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 ...
- 21
6
votes
2
answers
1k
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 ...
- 171
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 ...
- 104k
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-...
- 51
1
vote
1
answer
331
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 (...
25
votes
5
answers
48k
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 ...
- 351
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 ...
- 321