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3
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1answer
70 views

Should I reorder principal components after rotation?

I recently noticed that psych::principal reorders principal components on (automatic) rotation, according to their Eigenvalues (from highest to lowest). (Recall ...
5
votes
1answer
210 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 ...
5
votes
2answers
141 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 ...
2
votes
0answers
30 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
vote
1answer
46 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 ...
4
votes
1answer
86 views

What are “unrotated” and “rotated” principal components, given that PCA always rotates the coordinates axes?

As far as I understand, principal components are obtained by rotating the coordinate axes to align them with the directions of maximum variance. Nevertheless, I keep reading about "unrotated ...
4
votes
1answer
47 views

How to identify variables with significant loadings in principal component anlaysis

I have following example of principal component analysis using first 4 variables of iris data set (code in R): ...
0
votes
0answers
164 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): ...
1
vote
0answers
36 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 ...
2
votes
2answers
192 views

Strange results of varimax rotation of principal component analysis in Stata: rotated components are all zeros and ones

This is my initial output of Principal Component Analysis (PCA) using Stata and correlation matrix (because different scales and measurement units of inputs): ...
7
votes
1answer
335 views

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
0
votes
1answer
43 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 ...
0
votes
0answers
40 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 ...
1
vote
0answers
37 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. ...
4
votes
1answer
141 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 ...
0
votes
0answers
27 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 ...
1
vote
1answer
37 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
votes
2answers
708 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 ...
2
votes
0answers
47 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. ...
1
vote
1answer
2k 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 ...
0
votes
1answer
111 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
votes
1answer
119 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 ...
2
votes
2answers
1k 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 ...
7
votes
2answers
201 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 ...
0
votes
2answers
186 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
votes
1answer
212 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
votes
0answers
416 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 ...
4
votes
2answers
5k 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. ...
0
votes
2answers
136 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
votes
1answer
779 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
votes
1answer
81 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
vote
1answer
600 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 ...
1
vote
1answer
7k 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
votes
1answer
753 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
votes
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 ...
1
vote
0answers
302 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
votes
1answer
268 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 ...
3
votes
2answers
252 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 ...