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math::PCA(3tcl) Principal Components Analysis math::PCA(3tcl) 





NAME


math::PCA - Package for Principal Component Analysis






SYNOPSIS


package require Tcl ?8.6 9?


package require math::linearalgebra 1.1


::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?










DESCRIPTION


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.






COMMANDS


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.







  

  
- A list of observations (see the example below).

  

  
- 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.







  

  
- The number of components to be retained

  

  
- 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.







  

  
- 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.







  

  
- 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







  

  
- The values for the observation.







  
$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.







  

  
- The values for the observation.







  
$pca distance observation

  
Return the distance between the given observation and its approximation.
      (Note: this distance is based on the normalised vectors.)







  

  
- The values for the observation.







  
$pca qstatistic observation ?option?

  
Return the Q statistic, basically the square of the distance, for the
      given observation.







  

  
- The values for the observation.

  

  
- 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".










EXAMPLE


TODO: NIST example






BUGS, IDEAS, FEEDBACK


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.






KEYWORDS


PCA, math, statistics, tcl






CATEGORY


Mathematics







  

    1.1
    tcllib