source: trunk/yat/utility/PCA.h @ 1486

Last change on this file since 1486 was 1486, checked in by Jari Häkkinen, 13 years ago

Addresses #436.

  • 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 1486 2008-09-09 21:17:19Z jari $
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  Copyright (C) 2008 Peter Johansson
13
14  This file is part of the yat library, http://dev.thep.lu.se/yat
15
16  The yat library is free software; you can redistribute it and/or
17  modify it under the terms of the GNU General Public License as
18  published by the Free Software Foundation; either version 3 of the
19  License, or (at your option) any later version.
20
21  The yat library is distributed in the hope that it will be useful,
22  but WITHOUT ANY WARRANTY; without even the implied warranty of
23  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
24  General Public License for more details.
25
26  You should have received a copy of the GNU General Public License
27  along with this program; if not, write to the Free Software
28  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
29  02111-1307, USA.
30*/
31
32#include "Matrix.h"
33#include "Vector.h"
34
35namespace theplu {
36namespace yat {
37namespace utility {
38
39  /**
40     @brief Principal Component Analysis
41
42     Class performing PCA using SVD. This class assumes that
43     the columns corresponds to the dimenension of the problem.
44     That means if data has dimension NxM (M=columns) the number
45     of principal-axes will equal M-1. When projecting data into
46     this space, all Nx1 vectors will have dimension Mx1. Hence
47     the projection will have dimension MxM where each column is
48     a point in the new space. Also, it assumes that M>N. The opposite
49     problem is added in the functions: process_transposed_problem and
50     projection_transposed()...
51  */
52  class PCA
53  {
54  public:
55    /**
56       Constructor taking the data-matrix as input. No row-centering
57       should have been performed and no products.
58     */
59    explicit PCA(const utility::Matrix&);
60 
61    /**
62       If M<N use this method instead. Using the same format as before
63       where rows in the matrix corresponds to the dimensional coordinate.
64       The only difference is in the SVD step where the matrix V is used
65       after running the transposed matrix. For projections, see
66       projection_transposed() method.
67     */
68    //    void process_transposed_problem(void);
69
70    /**
71       \brief Returns eigenvalues in a utility::vector.
72
73       \return A const reference to the internal vector containing all
74       eigenvalues.
75    */
76    const utility::Vector& eigenvalues(void) const;
77
78    /**
79       \brief Get all eigenvectors in a utility::matrix.
80
81       \return A const reference to the internal matrix containing all
82       eigenvectors.
83    */
84    const utility::Matrix& eigenvectors(void) const;
85
86    /**
87       This function will project data onto the new coordinate-system
88       where the axes are the calculated eigenvectors. This means that
89       PCA must have been run before this function can be used!
90       Output is presented as coordinates in the N-dimensional room
91       spanned by the eigenvectors.
92    */
93    utility::Matrix projection( const utility::Matrix& ) const;
94
95    /**
96       Same as projection() but works when used
97       process_transposed_problem().
98    */
99    //    utility::matrix projection_transposed( const utility::matrix& ) const;
100
101
102  private:
103
104    /**
105       Will perform PCA according to the following scheme: \n
106       1: Rowcenter A  \n
107       2: SVD(A)  --> USV' \n
108       3: Calculate eigenvalues according to \n
109          \f$ \lambda_{ii} = s_{ii}/N_{rows} \f$ \n
110       4: Sort eigenvectors (from matrix V) according to descending eigenvalues\n
111    */
112    void process(void);
113
114    /**
115       Private function that will row-center the matrix A,
116       that is, A = A - M, where M is a matrix
117       with the meanvalues of each row
118    */
119    void row_center( utility::Matrix& A_center );
120
121    utility::Matrix A_; 
122    utility::Vector eigenvalues_;
123    utility::Matrix eigenvectors_;
124    utility::Vector meanvalues_;
125  };
126
127}}} // of namespace utility, yat, and theplu
128
129#endif
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