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Questions tagged [rotation]

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1answer
40 views

Gaussian distribution: moments, independence and rotation

I have a few questions with respect to the gaussian distribution, its moments and independence. So a gaussian distribution is fully specified by its first two moments, the mean and variance (or ...
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0answers
18 views

Good article examples of PAF/PCA

Can anyone give me (and probably to the rest of the world) good article examples which uses especially PAF (and/or PCA) factor analysis with oblique and/or orthogonal rotations?
0
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1answer
110 views

Which rotation type for principal component regression?

I would like to perform a principal component regression (PCR), but feel a little confused about the rotation type to be used in the principal component analysis (PCA) step. First I perform a PCA to ...
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0answers
32 views

Is PCA effectively just a rotation of the data, if you were to keep all principal components? [duplicate]

If so, why would you apply another rotation after you already found the "variance-maximizing" - and in that sense optimal - rotation. Wouldn't the second rotation lead to a - again - non-variane-...
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1answer
404 views

Oblique vs. Orthogonal Rotation for EFA

Will orthogonal relationships show up when using Oblique rotation? Based on the articles I have read on EFA rotation my understanding is that although oblique rotation procedures might be expected ...
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0answers
90 views

What is a rotation matrix and how to implemnt it?

In Revisiting the VLAD Image Representation the authors introduce Local Coordinate System, i.e. they: we learn off-line (for each visual word) a rotation matrix Qi from training descriptors mapped ...
3
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1answer
45 views

$\mathbf{Cov}(x,y)$ under rotation of axes

If $\mathbf{Cov}=0$ let $u=x \cdot cos(\theta)+y \cdot sin(\theta)$ and $v =y \cdot cos(\theta)-x \cdot sin(\theta)$. What will be $\mathbf{Cov}(u,v)$? Will it be $0$?
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0answers
215 views

How to use varimax rotated PCA to produce raster layers?

I have a raster stack of 19 layers called "raster_bio". The code to do PCA analysis is: ...
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0answers
321 views

linear regression after rotation

I have a set of 2 dimensional points [x,y], with a barycenter in 0,0 and I'm rotating it. I'm wondering why the linear regression of this set of points is not rotating of the same amplitude. Below ...
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2answers
605 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 ...
8
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1answer
35k views

Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix?

When doing a factor analysis (by principal axis factoring, for example) or a principal component analysis as factor analysis, and having performed an oblique rotation of the loadings, - which matrix ...
6
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2answers
5k views

Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?

I've been led to believe (see here and here) that Mahalanobis distance is the same as the Euclidean distance on the PCA-rotated data. In other words, taking multivariate normal data $X$, the ...
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0answers
91 views

How to organise an iterative manual rotation of n component pairs?

I am currently building a q.rotate() function for the qmethod R package for Q Methodology. As is desirable for Q, I'd like users to be able to iteratively rotate ...
1
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1answer
137 views

Does the order of rotations matter in rotating PCA loadings (by-hand)?

Suppose I have retained 3 principal components, and I want to rotate their loadings by hand (yeah, that's rare, but it is commonly used in Q Methodology). Does it matter in which order I rotate the ...
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0answers
2k views

Meaning of negative elements in Principal Component Analysis(PCA) rotated component matrix

Suppose that we have this rotated component matrix from PCA (SPSS output): ...
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0answers
742 views

How we can calculate squared factor loadings in Principal Component Analysis(PCA)?

This snapshot is from THIS article: What is Squared factor loadings and how we can calculate it. Any link between above snapshot and below snapshot of SPSS output? there isn't any relationship ...
0
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1answer
152 views

Isn't an oblique rotation against the whole spirit of principal component analysis?

I am studying principal component analysis (PCA) as a method to deal with multicollinearity. And when studying the rotation method -- which, if my understanding is correct, is the center of the PCA -...
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0answers
111 views

Different results based on two target rotation approaches

I am trying to do some data analyses based on target rotation in R using two different approaches. Here is a small simulation in r. ...
8
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1answer
2k views

How to generate uniformly random orthogonal matrices of positive determinant?

I've got probably a silly question about which, I must confess, I'm confused. Imagine repeated generating of uniformly distributed random orthogonal (orthonormal) matrix of some size $p$. Sometimes ...
1
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1answer
73 views

Statistical model for axis angle rotations

I would like to describe a large number of measurements of rotations $\textbf{x}_i$. Each rotation is described by its rotation axis $\textbf{v} =\frac{\textbf{x}}{|\textbf{x}|}$ and the rotation ...
4
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2answers
5k views

Why does my loading matrix following PCA with a varimax rotation contain only ones and zeros? [duplicate]

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2, center=TRUE, scale.=TRUE) So ...
3
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0answers
65 views

Are matrix Fisher r.v.s closed under multiplication?

With appropriate parameters, a matrix Fisher distribution provides a distribution over SO(3) (i.e. over rotations in $R^3$). See this MathOverflow post for a few notes describing the distribution. ...
9
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1answer
29k views

The difference between varimax and oblimin rotations in factor analysis

What is the difference between varimax rotation and oblimin rotation in factor analysis? Also, I am confused about the relationship between principal component analysis, varimax rotation and ...
3
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1answer
371 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 ...
0
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1answer
252 views

Varimax Rotated factors are very much NOT uncorrelated?

On the back of an earlier question i am having an issue. Software = SAS JMP Pro 11 Earlier Question My rotated factors (post Principal Components Analysis [PCA]) are not at all uncorrelated. I have ...
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2answers
8k views

Predict only the first N principal components in a PCA analysis

I'm using R to analyze a very large dataset. I conduct a PCA on one dataset, PCA <- prcomp(formula = ~., data = train, scale = T, na.action=na.exclude) and ...
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2answers
330 views

Extracting nonorthogonal sources in ICA/PCA/blind source seperation problem

My problem is essentially a 'blind source separation' problem. I have 3 non-orthogonal sources (or basis functions) and N random linear combinations (mixes) of said sources. My problem is to obtain ...
2
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1answer
587 views

Why direct oblimin rotation results in greater eigen values?

I came across this in the Wikipedia page about Factor Analysis. Is that true that direct oblimin rotation results in greater eigen values? If that is true, what's the reason behind it and does it ...
2
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0answers
771 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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2answers
225 views

How many PCs should varimax rotation be applied to?

I have a list of 25 air pollutants many of which are strongly correlated. I was hoping to reduce down to a short list of eigenvectors which would each be composed of a small number of the pollutants. ...
2
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1answer
302 views

A textbook error w.r.t structure and pattern loadings

I have this picture in Lattin representing structure and pattern loadings in factor analysis. If $Z$ (an observed variable) $=w_1 F_1+w_2 F_2$ (according to factor model), then the pattern loadings of ...
1
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1answer
1k views

To rotate or not to rotate post-PCA and pre-cluster analysis

Questions in respect to rotation post-PCA have been answered before -> its all in the hands of the researcher... Same answer to the question if rotation (orthogonal or not) makes sense before plugging ...
2
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2answers
16k views

Exploratory factor analysis - promax & factor cross-loadings

I have a question regarding the best practice for dealing with cross-loadings on factors after conducting an exploratory factor analysis using a promax rotation. Just to give a bit of background ...
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1answer
2k views

Is it acceptable to rotate factors with PCA for binary data?

What issues, if any, might there be in rotating factors in order to obtain factor/component loadings of binary data? Is it acceptable to rotate the factors when doing a traditional PCA? (Assuming I’m ...
5
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1answer
3k views

Can I somehow compute variance explained by PC after Oblique rotation in PCA?

Let´s say that my PCA analysis extracted 2 components, which explain 80% of the variance before rotation. The components were then rotated using oblique (Direct Oblimin) rotation, so SPSS cannot ...
3
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1answer
346 views

Detecting reflection in non-orthogonal rotation

I've known that, in orthogonal rotation, if the rotation matrix has determinant of -1 then reflection is present. Otherwise the determinant is +1 and we have pure rotation. May I extend this "sign-of-...
4
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2answers
328 views

Rotation matrices and prior invariance for arbitrary dimensions

I have a question about a rotation matrix, which can be represented in 2 dimensions as: $$R_{2}(\theta)=\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$$ For ...