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37 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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0answers
44 views

Different clustering for different rotation of PCA

i´m working on an application which is used for clustering. The process is done in SPSS. As the input-data can have a large number of variables/colummns as a pre-clustering step the PCA is run (via ...
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0answers
21 views

PCA (varimax normalized): are factor scores negative or positive?

When doing a Principal Component Analysis, with varimax rotations, we can get the factor scores based on correlations for each variable. These scores are either positive or negative, does it still ...
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53 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 ...
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1answer
111 views

How to obtain the same varimax-rotated PCA results in MATLAB and SPSS?

I'm trying to perform a PCA Extraction + Varimax Rotation in MATLAB and obtain the same results as in SPSS. My data is the following matrix A: ...
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1answer
3k 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
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2answers
225 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
48 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 ...
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1answer
58 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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1answer
59 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): ...
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596 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
63 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 ...
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2answers
431 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): ...
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1answer
54 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
65 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
48 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. ...
6
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1answer
389 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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1answer
44 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 ...
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2answers
1k 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 ...
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0answers
50 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
5k 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 ...
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1answer
129 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
136 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
2k 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
217 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
248 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 ...
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0answers
459 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
149 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. ...
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1answer
1k 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
91 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
698 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
9k 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
860 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
333 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
276 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
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2answers
261 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 ...