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1answer
32 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
11 views

Getting Rotation Matrix from SVD

I'd like to use SVD to get the rotation of ellipsoid data. When I create ellipsoid data with a known rotation, I can see that there is some kind of relationship between the $V'$ and the original ...
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0answers
32 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. ...
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1answer
64 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 ...
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0answers
19 views

SIFT rotation invariance

In Scale-Invariant Feature Transform, keypoints in an image are extracted which are invariant to scale, rotation and translation. The keypoints contain information on the scale and gradient of a given ...
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1answer
29 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 ...
3
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2answers
391 views

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

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2, center=TRUE, scale.=TRUE) So ...
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0answers
42 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. ...
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1answer
1k views

varimax rotation, Direct Oblimin and factor analysis

What is the difference between varimax rotation and direct oblimin in factor analysis? Also, I am confused the relationship among principal component analysis, varimax rotation and exploratory factor ...
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1answer
105 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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1answer
109 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
531 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
140 views

Is there a reason to leave an exploratory factor analysis solution unrotated?

Are there any reasons to not rotate an exploratory factor analysis solution? It's easy to find discussions comparing orthogonal solutions with oblique solutions, and I think I completely understand ...
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2answers
154 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
187 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
352 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
4k views

How to compute varimax-rotated principal components in R?

I have ran PCA on 25 variables and selected the top 7 PCs using prcomp. ...
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2answers
126 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. ...
4
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1answer
583 views

Using varimax-rotated PCA components as predictors in linear regression

After doing PCA, the first component describes the largest part of variability. This is important e.g. in study of body measurements where it is commonly known (Jolliffe, 2002) that PC1 axis captures ...
2
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1answer
76 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 ...
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1answer
520 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 ...
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1answer
6k 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 ...
3
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1answer
667 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 ...
3
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1answer
2k 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 ...
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0answers
286 views

How is the proof that the Quartimax/Varimax-rotation converges?

Empirically the quartimax-/varimax-rotation has proven useful and it was always converging in my applications. But from my readings years ago I have a vague remembering, that the fact of a proof of ...
3
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1answer
262 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 ...
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2answers
250 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 ...