source: trunk/yat/utility/PCA.h @ 1120

Last change on this file since 1120 was 1120, checked in by Peter, 14 years ago

vector is now Vector

  • Property svn:eol-style set to native
  • Property svn:keywords set to Author Date Id Revision
File size: 4.0 KB
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1#ifndef _theplu_yat_utility_pca_
2#define _theplu_yat_utility_pca_
3
4// $Id: PCA.h 1120 2008-02-21 23:18:41Z peter $
5
6/*
7  Copyright (C) 2003 Daniel Dalevi
8  Copyright (C) 2004 Jari Häkkinen
9  Copyright (C) 2005 Jari Häkkinen, Peter Johansson
10  Copyright (C) 2006 Jari Häkkinen
11  Copyright (C) 2007 Jari Häkkinen, Peter Johansson
12
13  This file is part of the yat library, http://trac.thep.lu.se/yat
14
15  The yat library is free software; you can redistribute it and/or
16  modify it under the terms of the GNU General Public License as
17  published by the Free Software Foundation; either version 2 of the
18  License, or (at your option) any later version.
19
20  The yat library is distributed in the hope that it will be useful,
21  but WITHOUT ANY WARRANTY; without even the implied warranty of
22  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
23  General Public License for more details.
24
25  You should have received a copy of the GNU General Public License
26  along with this program; if not, write to the Free Software
27  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
28  02111-1307, USA.
29*/
30
31#include "matrix.h"
32#include "Vector.h"
33
34namespace theplu {
35namespace yat {
36namespace utility {
37
38  /**
39     @brief Principal Component Analysis
40
41     Class performing PCA using SVD. This class assumes that
42     the columns corresponds to the dimenension of the problem.
43     That means if data has dimension NxM (M=columns) the number
44     of principal-axes will equal M-1. When projecting data into
45     this space, all Nx1 vectors will have dimension Mx1. Hence
46     the projection will have dimension MxM where each column is
47     a point in the new space. Also, it assumes that M>N. The opposite
48     problem is added in the functions: process_transposed_problem and
49     projection_transposed()...
50  */
51  class PCA
52  {
53  public:
54    /**
55       Constructor taking the data-matrix as input. No row-centering
56       should have been performed and no products.
57     */
58    explicit PCA(const utility::matrix&);
59 
60    /**
61       If M<N use this method instead. Using the same format as before
62       where rows in the matrix corresponds to the dimensional coordinate.
63       The only difference is in the SVD step where the matrix V is used
64       after running the transposed matrix. For projections, see
65       projection_transposed() method.
66     */
67    //    void process_transposed_problem(void);
68
69    /**
70       \brief Returns eigenvalues in a utility::vector.
71
72       \return A const reference to the internal vector containing all
73       eigenvalues.
74    */
75    const utility::Vector& eigenvalues(void) const;
76
77    /**
78       \brief Get all eigenvectors in a utility::matrix.
79
80       \return A const reference to the internal matrix containing all
81       eigenvectors.
82    */
83    const utility::matrix& eigenvectors(void) const;
84
85    /**
86       This function will project data onto the new coordinate-system
87       where the axes are the calculated eigenvectors. This means that
88       PCA must have been run before this function can be used!
89       Output is presented as coordinates in the N-dimensional room
90       spanned by the eigenvectors.
91    */
92    utility::matrix projection( const utility::matrix& ) const;
93
94    /**
95       Same as projection() but works when used
96       process_transposed_problem().
97    */
98    //    utility::matrix projection_transposed( const utility::matrix& ) const;
99
100
101  private:
102
103    /**
104       Will perform PCA according to the following scheme: \n
105       1: Rowcenter A  \n
106       2: SVD(A)  --> USV' \n
107       3: Calculate eigenvalues according to \n
108          \f$ \lambda_{ii} = s_{ii}/N_{rows} \f$ \n
109       4: Sort eigenvectors (from matrix V) according to descending eigenvalues\n
110    */
111    void process(void);
112
113    /**
114       Private function that will row-center the matrix A,
115       that is, A = A - M, where M is a matrix
116       with the meanvalues of each row
117    */
118    void row_center( utility::matrix& A_center );
119
120    utility::matrix A_; 
121    utility::Vector eigenvalues_;
122    utility::matrix eigenvectors_;
123    utility::Vector meanvalues_;
124  };
125
126}}} // of namespace utility, yat, and theplu
127
128#endif
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