source: trunk/c++_tools/statistics/ROC.h @ 650

Last change on this file since 650 was 650, checked in by Peter, 15 years ago

corrected documentation to be in line with guidinglines

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1#ifndef _theplu_statistics_roc_
2#define _theplu_statistics_roc_
3
4// $Id: ROC.h 650 2006-09-15 15:12:44Z peter $
5
6#include <c++_tools/classifier/Target.h>
7#include <c++_tools/statistics/Score.h>
8
9#include <utility>
10#include <vector>
11
12namespace theplu {
13  namespace utility {
14    class vector;
15  }
16namespace statistics { 
17
18  ///
19  /// Class for ROC (Reciever Operating Characteristic).
20  ///   
21  /// As the area under an ROC curve is equivalent to Mann-Whitney U
22  /// statistica, this class can be used to perform a Mann-Whitney
23  /// U-test (aka Wilcoxon).
24  ///
25  class ROC : public Score
26  {
27 
28  public:
29    ///
30    /// Default constructor
31    ///
32    ROC(bool absolute=true);
33         
34    ///
35    /// Destructor
36    ///
37    virtual ~ROC(void) {};
38         
39    /// Function taking \a value, \a target (+1 or -1) and vector
40    /// defining what samples to use. The score is equivalent to
41    /// Mann-Whitney statistics.
42    /// @return the area under the ROC curve. If the area is less
43    /// than 0.5 and absolute=true, 1-area is returned. Complexity is
44    /// \f$ N\log N \f$ where \f$ N \f$ is number of samples.
45    ///
46    double score(const classifier::Target& target, 
47                 const utility::vector& value); 
48   
49    /**
50        Function taking values, target, weight and a vector defining
51        what samples to use. The area is defines as \f$ \frac{\sum
52        w^+w^-}{\sum w^+w^-}\f$, where the sum in the numerator goes
53        over all pairs where value+ is larger than value-. The
54        denominator goes over all pairs. If target is equal to 1,
55        sample belonges to class + otherwise sample belongs to class
56        -. @return wheighted version of area under the ROC curve. If
57        the area is less than 0.5 and absolute=true, 1-area is
58        returned. Complexity is \f$ N^2 \f$ where \f$ N \f$ is number
59        of samples.
60    */
61    double score(const classifier::Target& target, 
62                 const classifier::DataLookupWeighted1D& value); 
63       
64
65    /**
66        Function taking values, target, weight and a vector defining
67        what samples to use. The area is defines as \f$ \frac{\sum
68        w^+w^-}{\sum w^+w^-}\f$, where the sum in the numerator goes
69        over all pairs where value+ is larger than value-. The
70        denominator goes over all pairs. If target is equal to 1,
71        sample belonges to class + otherwise sample belongs to class
72        -. @return wheighted version of area under the ROC curve. If
73        the area is less than 0.5 and absolute=true, 1-area is
74        returned. Complexity is \f$ N^2 \f$ where \f$ N \f$ is number
75        of samples.
76    */
77    double score(const classifier::Target& target, 
78                 const utility::vector& value, 
79                 const utility::vector& weight); 
80       
81
82    ///
83    ///Calculates the p-value, i.e. the probability of observing an
84    ///area equally or larger if the null hypothesis is true. If P is
85    ///near zero, this casts doubt on this hypothesis. The null
86    ///hypothesis is that the values from the 2 classes are generated
87    ///from 2 identical distributions. The alternative is that the
88    ///median of the first distribution is shifted from the median of
89    ///the second distribution by a non-zero amount. If the smallest
90    ///group size is larger than minimum_size (default = 10), then P
91    ///is calculated using a normal approximation.  @return the
92    ///one-sided p-value( if absolute true is used this is equivalent
93    ///to the two-sided p-value.)
94    ///
95    double p_value(void) const;
96   
97    ///
98    /// minimum_size is the threshold for when a normal
99    /// approximation is used for the p-value calculation.
100    ///
101    /// @return reference to minimum_size
102    ///
103    inline u_int& minimum_size(void){ return minimum_size_; } 
104
105    ///
106    /// Function returning true if target is positive (binary()) for
107    /// the sample with ith lowest data value, so i=0 corresponds to
108    /// the sample with the lowest data value and i=n()-1 the sample
109    /// with highest data value.
110    ///
111    bool target(const size_t i) const;
112
113    ///
114    /// @return number of samples
115    ///
116    inline size_t n(void) const { return vec_pair_.size(); }
117
118    ///
119    /// @return number of positive samples (Target.binary()==true)
120    ///
121    inline size_t n_pos(void) const { return nof_pos_; }
122
123  private:
124   
125    /// Implemented as in MatLab 13.1
126    double get_p_approx(const double) const;
127
128    /// Implemented as in MatLab 13.1
129    double get_p_exact(const double, const double, const double) const;
130
131    double area_;
132    u_int minimum_size_;
133    u_int nof_pos_;
134    std::vector<std::pair<bool, double> > vec_pair_; // class-value-pair
135  };
136
137  ///
138  /// The output operator for the ROC class. The output is an Nx2
139  /// matrix, where the first column is the sensitivity and second
140  /// is the specificity.
141  ///
142  std::ostream& operator<< (std::ostream& s, const ROC&);
143
144
145}} // of namespace statistics and namespace theplu
146
147#endif
148
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