Linked Questions
36 questions linked to/from PCA and Correspondence analysis in their relation to Biplot
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Relationship between SVD and PCA. How to use SVD to perform PCA?
Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
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7
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What are principal component scores?
What are principal component scores (PC scores, PCA scores)?
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108
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Loadings vs eigenvectors in PCA: when to use one or another?
In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$
I ...
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23
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2
answers
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Weighted principal components analysis
After some searching, I find very little on the incorporation of observation weights/measurement errors into principal components analysis. What I do find tends to rely on iterative approaches to ...
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1
answer
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Positioning the arrows on a PCA biplot
I am looking to implement a biplot for principal component analysis (PCA) in JavaScript. My question is, how do I determine the coordinates of the arrows from the $U,V,D$ output of the singular vector ...
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What is the proper association measure of a variable with a PCA component (on a biplot / loading plot)?
I am using FactoMineR to reduce my data set of measurements to the latent variables.
The variable map above is clear for me to interpret, but I am confused when ...
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1
answer
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Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analysis?
As per my understanding, in PCA based on correlations we get factor (= principal component in this instance) loadings which are nothing but the correlations between variables and factors. Now when I ...
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2
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What are the four axes on PCA biplot?
When you construct a biplot for a PCA analysis, you have principal component PC1 scores on the x-axis and PC2 scores on the y-axis. But what are the other two axes to the right and the top of the ...
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2
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Arrows of underlying variables in PCA biplot in R
At the risk of making the question software-specific, and with the excuse of its ubiquity and idiosyncrasies, I want to ask about the function biplot() in R, and, ...
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21
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1
answer
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Interpreting 2D correspondence analysis plots
I've been searching the internet far and wide... I have yet to find a really good overview of how to interpret 2D correspondence analysis plots. Could someone offer some advice on interpreting the ...
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1
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Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations?
I have a $20\times100$ matrix $X$, containing my $N=20$ samples in the $D=100$-dimensional space. I now wish to code up my own principal component analysis (PCA) in Matlab. I demean $X$ to $X_0$ first....
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Data space, variable space, observation space, model space (e.g. in linear regression)
Suppose we have the data matrix $\mathbf{X}$, which is $n$-by-$p$, and the label vector $Y$, which is $n$-by-one. Here, each row of the matrix is an observation, and each column corresponds to a ...
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1
answer
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(Multiple) Correspondence Analysis for count data entered as binary variables
I have a data set, 1014 cases and 55 variables which are binary and is in the form of
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2
answers
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How can one interpret the Stata output for Multiple Correspondence Analysis?
As an alternative to conducting exploratory factor analysis on a set of data, with binary responses, I have been suggested to use Multiple Correspondence Analysis (MCA).
Following is a curtailed and ...
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1
answer
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Q-mode vs. R-mode PCA
I have some doubts on Q-mode and R-mode principal component analysis (PCA). I've read from different sources that:
Q-mode PCA is equivalent to R-mode PCA of the transposed data matrix!
Q-mode PCA (...
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