Linked Questions

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
  • 103k
93 votes
7 answers

What are principal component scores?

What are principal component scores (PC scores, PCA scores)?
vrish88's user avatar
  • 1,213
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
23 votes
2 answers

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 ...
noname's user avatar
  • 520
24 votes
1 answer

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 ...
ktdrv's user avatar
  • 450
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
1 answer

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 ...
Kartikeya Pandey'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
21 votes
1 answer

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 ...
Brandon Bertelsen's user avatar
15 votes
1 answer

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....
Sibbs Gambling's user avatar
12 votes
1 answer

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 ...
user3813057's user avatar
  • 1,082
5 votes
1 answer

(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 ...
RS18's user avatar
  • 118
2 votes
2 answers

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 ...
May Ank's user avatar
  • 21
3 votes
1 answer

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 (...
Tiago's user avatar
  • 41

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