PCA Utilities

The PCA Utilities package provides small software routines for plotting PCA/OPLS scores and building dendrograms based on those scores. This page outlines how to install and use the pca-utils software.

Obtaining pca-utils

You can obtain the source code to pca-utils by clicking here.

Installing pca-utils

The PCA utilities are a set of command line open-source UNIX/Linux programs. The software is highly portable: provided your distribution has glibc, it should compile without incident. Once you have the source code, run these commands to install it:

cd /path/to/source/tarball
tar xf pca-utils-YYYYMMDD.tar.gz
cd pca-utils-YYYYMMDD/
make
sudo make install

By default, the programs install to /usr/bin, but you can easily change this by modifying the Makefile if you need to.

Plotting scores with ellipses

For an input list file called list.txt, you can quickly generate a postscript plot file (in this case called plot.ps) that shows your PCA scores with 95% confidence ellipses around each group:

pca-ellipses -1 44.4 -2 22.2 -i list.txt -o plot.ps

In the above statement, the optional arguments -1 and -2 were used to set contributions of PC1 and PC2 to 44.4% and 22.2%, respectively. You can then edit plot.ps to your liking. If you need a bit more control over your output, you can generate gnuplot-readable ellipses instead like so:

pca-ellipses -i list.txt > ellipses.txt
awk -F '\t' '/^[0-9]/{print$3,$4}' list.txt > points.txt
gnuplot> plot 'points.txt' w p, 'ellipses.txt' w l

Of course, in the second case, you're free to style everything any way you like. Happy hacking!

Generating dendrograms

Two complementary methods exist for generating trees. The first uses Euclidean distances and bootstrapping statistics, while the second uses Mahalanobis distances and p-values. For datasets containing well-separated groups in scores space, the bootstrapping method will do fine. However, highly separation in overlapped data may be better quantified with p-values in many cases.

Using bootstrapping

To build a simple tree that displays to the console for quick checks, just run something like this:

pca-bootstrap -i list.txt

The default number of bootstrap iterations is 100, but pca-bootstrap can easily handle more. You can set the number of iterations to, say 1000, like so:

pca-bootstrap -i list.txt -n 1000

Everything looks good? You can save a postscript file using the -o flag:

pca-bootstrap -i list.txt -n 1000 -o tree.ps

Using parameterizing

To build a simple tree that displays to the console for quick checks, just run something like this:

pca-dendrogram -i list.txt

Everything looks good? You can save a postscript file using the -o flag:

pca-dendrogram -i list.txt -o tree.ps

If everything works, the plots generated from these methods should look something like this:

+-----------------------------------------------------------George
|3.8e-11
|                      +-------------------------------------Ringo
+----------------------|1.3e-08
                       |                             +-----John
                       +-----------------------------|0.63
                                                     +------Paul

Use of pca-bootstrap will yield values at the nodes between 0 and 100, while pca-dendrogram will yield values between 0 and 1.

Calculating p-values

FIXME

Calculating basic statistics

If you're interested in basic information about each group, such as mean and/or covariance, you can use pca-stats:

pca-stats -i list.txt

Goodness, that was easy, wasn't it!?

Generating random datasets

Mainly provided for entertainment value and development/debugging, pca-rand lets you generate list files that contain bivariate normally distributed point sets. Here's an example command (in the bash scripting language) to build a faux list file:

(pca-rand -H -L John -u '(-2,2)' -v '(2,0.6)' -r 45 -n 10;
 pca-rand -L Paul -u '(-2,2)' -v '(2,0.6)' -r 135 -n 9;
 pca-rand -L George -u '(3,-2)' -v '(4,3)' -r 120 -n 13;
 pca-rand -L Ringo -u '(-1,-1)' -v '(2,2)' -r 0 -n 15) > list.txt

No, you read that right. You can download the list file generated by a single run of this command here: File:Beatles.txt.

"Wait, I'm still confused"

Remember that every command in the pca-utils package has a help message. Just run the command that you need information on with the --help flag to get a nice message on how to use that command.