238k views

### 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 ...
203k views

### What are principal component scores?

What are principal component scores (PC scores, PCA scores)?
115k views

### 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 ...
15k views

### 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 ...
9k views

### 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 ...
34k views

### 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 ...
13k views

### 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 ...
15k views

### 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 ...
15k views

### 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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### 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....
9k views

### 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, ...
5k views

### 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 ...
8k views

### (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 ...
4k views

### 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 ...
760 views

### When you do PCA (or any dimensionality reduction), what is “the number of dimensions”?

Fundamental question When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? I always thought that the thing you measure (ie, the variable) is the number of dimensions: ...

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