Linked Questions

2 votes
0 answers

Varying lengths of eigenvectors on a PCA biplot [duplicate]

I'm conducting a PCA in Matlab on standardized variables. My goal is to interpret angles = loadings, correlations bw. variables and PC-axis directions = vectors point to the direction of the ...
Just_Sveta's user avatar
0 votes
1 answer

what does the length of arrows represent in the correlation circle plot in pca analysis? [duplicate]

I want to know that in PCA analysis or FAMD the lengths of arrows in correlation circle plot(which can be plotted by bellow code) is equal to which parameter(coefficient estimates,cos2,contribution,......
far's user avatar
  • 121
1 vote
0 answers

When plotting PCA analysis with loadings on top, loading arrows come out way too short [duplicate]

I am trying to make a reasonable looking PCA analysis, where not only data are projected in two axis, but also the loadings of the data are projected on top of the data. Similar to the following ...
Areza's user avatar
  • 1,128
0 votes
0 answers

Does biplot() function in R use rotations or loadings to plot arrows? [duplicate]

For following code performing principal component analysis: ...
rnso's user avatar
  • 9,517
591 votes
4 answers

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 ...
amoeba's user avatar
  • 102k
108 votes
5 answers

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 ...
user2696565's user avatar
  • 1,379
33 votes
3 answers

Visualizing a million, PCA edition

Is it possible to visualize the output of Principal Component Analysis in ways that give more insight than just summary tables? Is it possible to do it when the number of observations is large, say ~...
gappy's user avatar
  • 5,490
37 votes
2 answers

Interpretation of biplots in principal components analysis

I came across this nice tutorial: A Handbook of Statistical Analyses Using R. Chapter 13. Principal Component Analysis: The Olympic Heptathlon on how to do PCA in R language. I don't understand the ...
user862's user avatar
  • 2,709
45 votes
1 answer

PCA and Correspondence analysis in their relation to Biplot

Biplot is often used to display results of principal component analysis (and of related techniques). It is a dual or overlay scatterplot showing component loadings and component scores simultaneously. ...
ttnphns's user avatar
  • 56.4k
21 votes
1 answer

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 ...
Fredrik Karlsson's user avatar
24 votes
2 answers

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 ...
Nils's user avatar
  • 241
13 votes
2 answers

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, ...
Antoni Parellada's user avatar
13 votes
1 answer

What is the difference between "loadings" and "correlation loadings" in PCA and PLS?

One common thing to do when doing Principal Component Analysis (PCA) is to plot two loadings against each other to investigate the relationships between the variables. In the paper accompanying the ...
user1593755's user avatar
10 votes
2 answers

Conclusions from output of a principal component analysis

I am trying to understand output of principal component analysis performed as follows: ...
rnso's user avatar
  • 9,517
4 votes
1 answer

When to use distance biplot vs. correlation biplot in PCA

I wonder what could be good examples of using scaling 1 and 2 for a principal component analysis biplot. By examples, I mean ecological examples or applied examples of the PCA scaling so that one can ...
M. Beausoleil's user avatar

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