1math::PCA(n) Principal Components Analysis math::PCA(n)
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8 math::PCA - Package for Principal Component Analysis
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11 package require Tcl ?8.6?
12 package require math::linearalgebra 1.0
14 ::math::PCA::createPCA data ?args?
16 $pca using ?number?|?-minproportion value?
18 $pca eigenvectors ?option?
20 $pca eigenvalues ?option?
22 $pca proportions ?option?
24 $pca approximate observation
26 $pca approximatOriginal
28 $pca scores observation
30 $pca distance observation
32 $pca qstatistic observation ?option?
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38 The PCA package provides a means to perform principal components analy‐
39 sis in Tcl, using an object-oriented technique as facilitated by TclOO.
40 It actually defines a single public method, ::math::PCA::createPCA,
41 which constructs an object based on the data that are passed to perform
42 the actual analysis.
43 The methods of the PCA objects that are created with this command allow
45 one to examine the principal components, to approximate (new) observa‐
46 tions using all or a selected number of components only and to examine
47 the properties of the components and the statistics of the approxima‐
48 tions.
49 The package has been modelled after the PCA example provided by the
51 original linear algebra package by Ed Hume.
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54 The math::PCA package provides one public command:
55 ::math::PCA::createPCA data ?args?
57 Create a new object, based on the data that are passed via the
58 data argument. The principal components may be based on either
59 correlations or covariances. All observations will be nor‐
60 malised according to the mean and standard deviation of the
61 original data.
62 list data
64 - A list of observations (see the example below).
65 list args
67 - A list of key-value pairs defining the options. Cur‐
68 rently there is only one key: -covariances. This indi‐
69 cates if covariances are to be used (if the value is 1)
70 or instead correlations (value is 0). The default is to
71 use correlations.
72 The PCA object that is created has the following methods:
74 $pca using ?number?|?-minproportion value?
76 Set the number of components to be used in the analysis (the
77 number of retained components). Returns the number of compo‐
78 nents, also if no argument is given.
79 int number
81 - The number of components to be retained
82 double value
84 - Select the number of components based on the minimum
85 proportion of variation that is retained by them. Should
86 be a value between 0 and 1.
87 $pca eigenvectors ?option?
89 Return the eigenvectors as a list of lists.
90 string option
92 - By default only the retained components are returned.
93 If all eigenvectors are required, use the option -all.
94 $pca eigenvalues ?option?
96 Return the eigenvalues as a list of lists.
97 string option
99 - By default only the eigenvalues of the retained compo‐
100 nents are returned. If all eigenvalues are required, use
101 the option -all.
102 $pca proportions ?option?
104 Return the proportions for all components, that is, the amount
105 of variations that each components can explain.
106 $pca approximate observation
108 Return an approximation of the observation based on the retained
109 components
110 list observation
112 - The values for the observation.
113 $pca approximatOriginal
115 Return an approximation of the original data, using the retained
116 components. It is a convenience method that works on the com‐
117 plete set of original data.
118 $pca scores observation
120 Return the scores per retained component for the given observa‐
121 tion.
122 list observation
124 - The values for the observation.
125 $pca distance observation
127 Return the distance between the given observation and its ap‐
128 proximation. (Note: this distance is based on the normalised
129 vectors.)
130 list observation
132 - The values for the observation.
133 $pca qstatistic observation ?option?
135 Return the Q statistic, basically the square of the distance,
136 for the given observation.
137 list observation
139 - The values for the observation.
140 string option
142 - If the observation is part of the original data, you
143 may want to use the corrected Q statistic. This is
144 achieved with the option "-original".
145
147 TODO: NIST example
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150 This document, and the package it describes, will undoubtedly contain
151 bugs and other problems. Please report such in the category PCA of the
152 Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist]. Please also
153 report any ideas for enhancements you may have for either package
154 and/or documentation.
155 When proposing code changes, please provide unified diffs, i.e the out‐
157 put of diff -u.
158 Note further that attachments are strongly preferred over inlined
160 patches. Attachments can be made by going to the Edit form of the
161 ticket immediately after its creation, and then using the left-most
162 button in the secondary navigation bar.
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165 PCA, math, statistics, tcl
166
168 Mathematics
169tcllib 1.0 math::PCA(n)