2k views

### 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 ...
734 views

### Selecting subset of variables most associated with the principal components of the data [duplicate]

I have a large data matrix that I'm trying to reduce to a reasonably sized basis set. The original matrix is 916x225, and I need to reduce the number of variables (its columns) to around 50, but I ...
595k views

### Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
230k views

### What are the differences between Factor Analysis and Principal Component Analysis?

It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...
120k views

### PCA on correlation or covariance?

What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
13k views

### Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
21k views

### How to visualize what canonical correlation analysis does (in comparison to what principal component analysis does)?

Canonical correlation analysis (CCA) is a technique related to principal component analysis (PCA). While it is easy to teach PCA or linear regression using a scatter plot (see a few thousand examples ...
112k 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 ...
14k views

### How does Factor Analysis explain the covariance while PCA explains the variance?

Here is a quote from Bishop's "Pattern Recognition and Machine Learning" book, section 12.2.4 "Factor analysis": According to the highlighted part, factor analysis captures the covariance between ...
49k views

### PCA on correlation or covariance: does PCA on correlation ever make sense? [closed]

In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components (from their respective eigenvectors). These give different results (...
13k views

### 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. ...
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 ...
13k views

### Converting similarity matrix to (euclidean) distance matrix

In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment ...