math::PCA - Package for Principal Component Analysis
package require Tcl ?8.6?
package require math::linearalgebra 1.0
::math::PCA::createPCA data ?args?
$pca using ?number?|?-minproportion value?
$pca eigenvectors ?option?
$pca eigenvalues ?option?
$pca proportions ?option?
$pca approximate observation
$pca approximatOriginal
$pca scores observation
$pca distance observation
$pca qstatistic observation ?option?
The PCA package provides a means to perform principal components
analysis in Tcl, using an object-oriented technique as facilitated by TclOO.
It actually defines a single public method, ::math::PCA::createPCA,
which constructs an object based on the data that are passed to perform the
actual analysis.
The methods of the PCA objects that are created with this command
allow one to examine the principal components, to approximate (new)
observations using all or a selected number of components only and to
examine the properties of the components and the statistics of the
approximations.
The package has been modelled after the PCA example provided by
the original linear algebra package by Ed Hume.
The math::PCA package provides one public command:
- ::math::PCA::createPCA data ?args?
- Create a new object, based on the data that are passed via the data
argument. The principal components may be based on either correlations or
covariances. All observations will be normalised according to the mean and
standard deviation of the original data.
- list data
- - A list of observations (see the example below).
- list args
- - A list of key-value pairs defining the options. Currently there is only
one key: -covariances. This indicates if covariances are to be used
(if the value is 1) or instead correlations (value is 0). The default is
to use correlations.
The PCA object that is created has the following methods:
- $pca using ?number?|?-minproportion value?
- Set the number of components to be used in the analysis (the number of
retained components). Returns the number of components, also if no
argument is given.
- int number
- - The number of components to be retained
- double
value
- - Select the number of components based on the minimum proportion of
variation that is retained by them. Should be a value between 0 and
1.
- $pca eigenvectors ?option?
- Return the eigenvectors as a list of lists.
- string
option
- - By default only the retained components are returned. If all
eigenvectors are required, use the option -all.
- $pca eigenvalues ?option?
- Return the eigenvalues as a list of lists.
- string
option
- - By default only the eigenvalues of the retained components are
returned. If all eigenvalues are required, use the option
-all.
- $pca proportions ?option?
- Return the proportions for all components, that is, the amount of
variations that each components can explain.
- $pca approximate observation
- Return an approximation of the observation based on the retained
components
- $pca approximatOriginal
- Return an approximation of the original data, using the retained
components. It is a convenience method that works on the complete set of
original data.
- $pca scores observation
- Return the scores per retained component for the given observation.
- $pca distance observation
- Return the distance between the given observation and its approximation.
(Note: this distance is based on the normalised vectors.)
- $pca qstatistic observation ?option?
- Return the Q statistic, basically the square of the distance, for the
given observation.
- list
observation
- - The values for the observation.
- string
option
- - If the observation is part of the original data, you may want to use the
corrected Q statistic. This is achieved with the option
"-original".
This document, and the package it describes, will undoubtedly
contain bugs and other problems. Please report such in the category
PCA of the Tcllib Trackers
[http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for
enhancements you may have for either package and/or documentation.
When proposing code changes, please provide unified diffs,
i.e the output of diff -u.
Note further that attachments are strongly preferred over
inlined patches. Attachments can be made by going to the Edit form of
the ticket immediately after its creation, and then using the left-most
button in the secondary navigation bar.
PCA, math, statistics, tcl