1 | #ifndef _theplu_yat_normalizer_qquantile_normalizer_ |
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2 | #define _theplu_yat_normalizer_qquantile_normalizer_ |
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3 | |
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4 | /* |
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5 | Copyright (C) 2009 Jari Häkkinen, Peter Johansson |
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6 | Copyright (C) 2010 Peter Johansson |
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7 | |
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8 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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9 | |
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10 | The yat library is free software; you can redistribute it and/or |
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11 | modify it under the terms of the GNU General Public License as |
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12 | published by the Free Software Foundation; either version 3 of the |
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13 | License, or (at your option) any later version. |
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14 | |
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15 | The yat library is distributed in the hope that it will be useful, |
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16 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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18 | General Public License for more details. |
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19 | |
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20 | You should have received a copy of the GNU General Public License |
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21 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
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22 | */ |
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23 | |
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24 | #include "utility.h" |
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25 | |
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26 | #include "yat/regression/CSplineInterpolation.h" |
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27 | #include "yat/utility/concept_check.h" |
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28 | #include "yat/utility/DataIterator.h" |
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29 | #include "yat/utility/DataWeight.h" |
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30 | #include "yat/utility/Exception.h" |
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31 | #include "yat/utility/iterator_traits.h" |
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32 | #include "yat/utility/sort_index.h" |
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33 | #include "yat/utility/Vector.h" |
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34 | #include "yat/utility/WeightIterator.h" |
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35 | #include "yat/utility/yat_assert.h" |
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36 | |
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37 | #include <boost/concept_check.hpp> |
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38 | |
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39 | #include <algorithm> |
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40 | #include <cmath> |
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41 | #include <iterator> |
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42 | #include <limits> |
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43 | #include <numeric> |
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44 | #include <stdexcept> |
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45 | #include <vector> |
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46 | |
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47 | namespace theplu { |
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48 | namespace yat { |
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49 | namespace utility { |
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50 | class VectorBase; |
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51 | } |
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52 | namespace normalizer { |
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53 | |
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54 | /** |
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55 | \brief Perform Q-quantile normalization |
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56 | |
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57 | Perform a Q-quantile normalization on a \a source range, after |
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58 | which it will approximately have the same distribution of data as |
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59 | the \a target range (the Q-quantiles are the same). The rank of |
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60 | an element in the \a source range is not changed. |
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61 | |
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62 | The class works also with unweighed ranges, and there is no |
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63 | restriction that weighted \a source range requires weighted \a |
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64 | target range or vice versa. |
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65 | |
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66 | Normalization goes like this: |
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67 | - Data are not assumed to be sorted. |
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68 | - Partition sorted \a target data in Q parts. Q must be 3 or larger |
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69 | because of requirements from the underlying cubic spline fit |
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70 | - Calculate the arithmetic (weighted) mean for each part, the mean is |
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71 | assigned to the mid point of each part. |
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72 | - Do the above for the data to be transformed (called \a source |
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73 | here). |
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74 | - For each part, calculate the difference between the \a target |
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75 | and \a the source. Now we have \a Q differences \f$ d_i \f$ |
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76 | with associated rank (midpoint of each part). |
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77 | - Create a cubic spline fit to this difference vector \a d. The |
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78 | resulting curve is used to recalculate all values in \a source. |
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79 | - Use the cubic spline fit for values within the cubic spline |
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80 | fit range [midpoint 1st part, midpoint last part]. |
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81 | - For data outside the cubic spline fit use linear |
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82 | extrapolation, i.e., a constant shift. \f$ d_{first} \f$ for |
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83 | points below fit range, and \f$ d_{last} \f$ for points above fit |
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84 | range. |
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85 | |
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86 | \since New in yat 0.5 |
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87 | */ |
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88 | class qQuantileNormalizer |
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89 | { |
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90 | public: |
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91 | /** |
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92 | \brief Constructor |
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93 | |
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94 | Divides a sorted copy of range [\a first,\a last) into \a Q |
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95 | parts. Parts are divided such that the sum of weights is |
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96 | approximately the same in the different parts. If a relative |
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97 | weight, \f$ w_i / \sum w_i \f$, is larger than 1/Q this might |
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98 | be difficult to achieve, in which case a an exception is |
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99 | thrown. In the unweighted case this implies that \a Q should be |
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100 | smaller (or equal) than number of elements in [\a first, \a |
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101 | last). |
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102 | |
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103 | The range supplied to the constructor sets the target |
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104 | distribution. |
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105 | |
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106 | As the \a source range is also divided into \a Q parts (when |
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107 | operator() is called), it is recommended to keep \a Q smaller |
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108 | (or equal) than the size of ranges that will be normalized. |
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109 | |
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110 | Also, \a Q must not be smaller than 3 due to restrictions in |
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111 | the cubic spline fit utilized in the normalization. |
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112 | |
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113 | \b Type \b Requirements: |
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114 | - \c ForwardIterator is a model of \forward_traversal_iterator |
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115 | - \c ForwardIterator is a \ref concept_data_iterator |
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116 | */ |
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117 | template<typename ForwardIterator> |
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118 | qQuantileNormalizer(ForwardIterator first, ForwardIterator last, |
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119 | unsigned int Q); |
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120 | |
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121 | /** |
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122 | \brief Perform the Q-quantile normalization. |
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123 | |
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124 | Elements in [\a first, \a last) are normalized as described |
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125 | above and the result is assigned to [\a result, \a result + \a |
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126 | last-\a first). Input range [\a first, \a last) is not |
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127 | modified. If ranges are weighted, the weights are copied from |
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128 | [\a first, \a last) to \a result range. |
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129 | |
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130 | It is possible to normalize "in place"; it is permissible for |
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131 | \a first and \a result to be the same. However, as assignment |
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132 | occurs sequentially, the operation is undefined if \a result is |
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133 | the same as any in range [\a first, \a last). |
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134 | |
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135 | \b Type Requirements: |
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136 | - \c RandomAccessIterator1 is a \ref concept_data_iterator |
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137 | - \c RandomAccessIterator1 is a \random_access_traversal_iterator |
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138 | - \c RandomAccessIterator2 is a \ref concept_data_iterator |
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139 | - \c RandomAccessIterator2 is a \random_access_traversal_iterator |
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140 | - \c RandomAccessIterator2 is a \writable_iterator |
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141 | |
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142 | */ |
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143 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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144 | void operator()(RandomAccessIterator1 first, RandomAccessIterator1 last, |
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145 | RandomAccessIterator2 result) const; |
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146 | |
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147 | private: |
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148 | |
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149 | /** |
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150 | \brief Partition a range of data into equal sizes. |
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151 | |
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152 | Copy the range [first, last), sort the copy, and divide the |
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153 | sorted copy in Q parts. The parts are created such that the total |
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154 | weight in a part is approximately W/Q where W is the total weight |
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155 | (over all parts). The class calculates the average value in each |
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156 | part and also the "quantile". |
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157 | */ |
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158 | class Partitioner |
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159 | { |
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160 | public: |
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161 | /** |
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162 | \brief Create the partition and perform required calculations. |
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163 | */ |
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164 | template<typename ForwardIterator> |
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165 | Partitioner(ForwardIterator first, ForwardIterator last, |
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166 | unsigned int N); |
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167 | |
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168 | /** |
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169 | \brief Return the averages for each part. |
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170 | |
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171 | \return The average vector. |
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172 | */ |
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173 | const utility::Vector& averages(void) const; |
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174 | |
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175 | /** |
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176 | The quantile (here) is defined as (w_lower + w_upper) / 2W, |
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177 | where w_lower is the total weight of elements smaller than the |
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178 | smallest element in the part, and w_upper is the total weight |
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179 | of elements smaller (or equal) than the largest value in the |
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180 | part. |
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181 | |
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182 | In the unweighted case all weights are 1.0, which implies q_0 = |
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183 | n_0/N, q_1 = (n_0+n_1/2)/N, q_2 = (n_0+n_1+n_2/2)/N where n_i |
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184 | is number of elements in ith part. |
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185 | |
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186 | \return The quantiles vector. |
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187 | */ |
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188 | const utility::Vector& quantiles(void) const; |
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189 | |
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190 | /** |
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191 | \return The number of parts. |
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192 | */ |
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193 | size_t size(void) const; |
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194 | |
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195 | private: |
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196 | // unweighted "constructor" |
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197 | template<typename ForwardIterator> |
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198 | void build(ForwardIterator first, ForwardIterator last, unsigned int N, |
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199 | utility::unweighted_iterator_tag); |
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200 | // weighted "constructor" |
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201 | template<typename ForwardIterator> |
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202 | void build(ForwardIterator first, ForwardIterator last, unsigned int N, |
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203 | utility::weighted_iterator_tag); |
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204 | void init(const utility::VectorBase&, unsigned int N); |
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205 | void init(const std::vector<utility::DataWeight>&, unsigned int N); |
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206 | |
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207 | utility::Vector average_; |
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208 | utility::Vector quantiles_; |
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209 | }; |
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210 | |
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211 | Partitioner target_; |
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212 | |
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213 | // unweighted version |
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214 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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215 | void normalize(const Partitioner& source,RandomAccessIterator1 first, |
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216 | RandomAccessIterator1 last, RandomAccessIterator2 result, |
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217 | utility::unweighted_iterator_tag tag) const; |
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218 | |
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219 | // weighted version |
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220 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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221 | void normalize(const Partitioner& source,RandomAccessIterator1 first, |
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222 | RandomAccessIterator1 last, RandomAccessIterator2 result, |
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223 | utility::weighted_iterator_tag tag) const; |
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224 | }; |
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225 | |
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226 | |
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227 | // template implementations |
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228 | |
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229 | template<typename ForwardIterator> |
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230 | qQuantileNormalizer::qQuantileNormalizer(ForwardIterator first, |
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231 | ForwardIterator last, |
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232 | unsigned int Q) |
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233 | : target_(Partitioner(first, last, Q)) |
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234 | { |
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235 | YAT_ASSERT(Q>2); |
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236 | } |
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237 | |
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238 | |
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239 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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240 | void qQuantileNormalizer::operator()(RandomAccessIterator1 first, |
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241 | RandomAccessIterator1 last, |
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242 | RandomAccessIterator2 result) const |
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243 | { |
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244 | BOOST_CONCEPT_ASSERT((utility::DataIterator<RandomAccessIterator1>)); |
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245 | using boost_concepts::RandomAccessTraversal; |
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246 | BOOST_CONCEPT_ASSERT((RandomAccessTraversal<RandomAccessIterator1>)); |
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247 | BOOST_CONCEPT_ASSERT((utility::DataIterator<RandomAccessIterator2>)); |
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248 | BOOST_CONCEPT_ASSERT((RandomAccessTraversal<RandomAccessIterator2>)); |
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249 | using boost_concepts::WritableIterator; |
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250 | BOOST_CONCEPT_ASSERT((WritableIterator<RandomAccessIterator2>)); |
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251 | |
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252 | Partitioner source(first, last, target_.size()); |
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253 | typename utility::weighted_if_any2<RandomAccessIterator1, RandomAccessIterator2>::type tag; |
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254 | normalize(source, first, last, result, tag); |
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255 | } |
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256 | |
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257 | |
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258 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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259 | void |
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260 | qQuantileNormalizer::normalize(const qQuantileNormalizer::Partitioner& source, |
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261 | RandomAccessIterator1 first, |
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262 | RandomAccessIterator1 last, |
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263 | RandomAccessIterator2 result, |
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264 | utility::unweighted_iterator_tag tag) const |
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265 | { |
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266 | utility::check_iterator_is_unweighted(first); |
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267 | utility::check_iterator_is_unweighted(result); |
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268 | size_t N = last-first; |
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269 | YAT_ASSERT(N >= target_.size()); |
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270 | |
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271 | std::vector<size_t> sorted_index(last-first); |
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272 | utility::sort_index(first, last, sorted_index); |
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273 | |
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274 | utility::Vector diff(source.averages()); |
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275 | diff-=target_.averages(); |
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276 | const utility::Vector& idx=target_.quantiles(); |
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277 | regression::CSplineInterpolation cspline(idx,diff); |
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278 | |
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279 | // linear extrapolation for first part, i.e., use first diff for |
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280 | // all points in the first part. |
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281 | size_t start=0; |
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282 | size_t end = static_cast<size_t>(std::ceil(N*idx(0) - 0.5)); |
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283 | // take care of limiting case number of parts approximately equal |
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284 | // to the number of elements in range. |
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285 | if (end==0) |
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286 | ++end; |
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287 | for (size_t i=start; i<end; ++i) { |
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288 | size_t si = sorted_index[i]; |
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289 | result[si] = first[si] - diff(0); |
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290 | } |
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291 | |
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292 | using utility::yat_assert; |
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293 | |
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294 | // cspline interpolation for all data between the mid points of |
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295 | // the first and last part |
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296 | start=end; |
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297 | end = static_cast<size_t>(std::ceil(N*idx(idx.size()-1) - 0.5)); |
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298 | if (end>=N) |
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299 | end = N-1; |
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300 | for ( size_t i=start; i<end; ++i) { |
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301 | size_t si = sorted_index[i]; |
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302 | |
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303 | YAT_ASSERT((i+0.5)/N>idx(0)); |
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304 | result[si] = first[si] - cspline.evaluate((i+0.5)/N); |
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305 | } |
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306 | |
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307 | // linear extrapolation for last part, i.e., use last diff for |
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308 | // all points in the last part. |
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309 | for (size_t i=end ; i<N; ++i) { |
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310 | size_t si = sorted_index[i]; |
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311 | result[si] = first[si] - diff(diff.size()-1); |
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312 | } |
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313 | } |
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314 | |
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315 | |
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316 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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317 | void qQuantileNormalizer::normalize(const Partitioner& source, |
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318 | RandomAccessIterator1 first, |
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319 | RandomAccessIterator1 last, |
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320 | RandomAccessIterator2 result, |
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321 | utility::weighted_iterator_tag tag) const |
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322 | { |
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323 | // copy the weights |
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324 | detail::copy_weight_if_weighted(first, last, result); |
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325 | |
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326 | double total_w = std::accumulate(utility::weight_iterator(first), |
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327 | utility::weight_iterator(last), 0.0); |
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328 | |
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329 | std::vector<size_t> sorted_index(last-first); |
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330 | // Code to avoid problems with NaN (ticket:535) |
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331 | // utility::sort_index(utility::data_iterator(first), |
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332 | // utility::data_iterator(last), sorted_index); |
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333 | // ... above statement replaced below code block |
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334 | { |
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335 | using namespace utility; |
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336 | std::vector<double> vec; |
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337 | vec.reserve(std::distance(first, last)); |
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338 | std::copy(utility::data_iterator(first), utility::data_iterator(last), |
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339 | std::back_inserter(vec)); |
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340 | for (std::vector<double>::iterator i(vec.begin()); i!=vec.end(); ++i) |
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341 | if (std::isnan(*i)) |
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342 | *i = std::numeric_limits<double>::infinity(); |
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343 | utility::sort_index(vec.begin(), vec.end(), sorted_index); |
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344 | } |
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345 | // end Code to avoid problems with NaN (ticket:535) |
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346 | |
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347 | utility::Vector diff(source.averages()); |
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348 | diff-=target_.averages(); |
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349 | const utility::Vector& idx=target_.quantiles(); |
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350 | regression::CSplineInterpolation cspline(idx,diff); |
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351 | |
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352 | double sum_w=0; |
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353 | utility::iterator_traits<RandomAccessIterator1> traits1; |
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354 | utility::iterator_traits<RandomAccessIterator2> traits2; |
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355 | for (size_t i=0; i<sorted_index.size(); ++i) { |
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356 | size_t si = sorted_index[i]; |
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357 | double w = (sum_w + 0.5*traits1.weight(first+si))/total_w; |
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358 | double correction = 0; |
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359 | if (w <= idx(0)) { |
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360 | // linear extrapolation for first part, i.e., use first diff for |
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361 | // all points in the first part. |
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362 | correction = diff(0); |
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363 | } |
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364 | else if (w < idx(idx.size()-1) ) { |
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365 | // cspline interpolation for all data between the mid points of |
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366 | // the first and last part |
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367 | correction = cspline.evaluate(w); |
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368 | } |
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369 | else { |
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370 | // linear extrapolation for last part, i.e., use last diff for |
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371 | // all points in the last part. |
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372 | correction = diff(diff.size()-1); |
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373 | } |
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374 | traits2.data(result+si) = traits1.data(first+si) - correction; |
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375 | sum_w += traits1.weight(first+si); |
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376 | } |
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377 | } |
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378 | |
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379 | |
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380 | template<typename ForwardIterator> |
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381 | qQuantileNormalizer::Partitioner::Partitioner(ForwardIterator first, |
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382 | ForwardIterator last, |
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383 | unsigned int N) |
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384 | : average_(utility::Vector(N)), quantiles_(utility::Vector(N)) |
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385 | { |
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386 | BOOST_CONCEPT_ASSERT((boost_concepts::ForwardTraversal<ForwardIterator>)); |
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387 | BOOST_CONCEPT_ASSERT((utility::DataIterator<ForwardIterator>)); |
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388 | build(first, last, N, |
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389 | typename utility::weighted_iterator_traits<ForwardIterator>::type()); |
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390 | } |
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391 | |
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392 | |
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393 | template<typename ForwardIterator> |
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394 | void qQuantileNormalizer::Partitioner::build(ForwardIterator first, |
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395 | ForwardIterator last, |
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396 | unsigned int N, |
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397 | utility::unweighted_iterator_tag) |
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398 | { |
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399 | utility::Vector vec(std::distance(first, last)); |
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400 | std::copy(first, last, vec.begin()); |
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401 | std::sort(vec.begin(), vec.end()); |
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402 | init(vec, N); |
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403 | } |
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404 | |
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405 | |
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406 | template<typename ForwardIterator> |
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407 | void qQuantileNormalizer::Partitioner::build(ForwardIterator first, |
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408 | ForwardIterator last, |
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409 | unsigned int N, |
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410 | utility::weighted_iterator_tag) |
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411 | { |
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412 | using namespace utility; |
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413 | std::vector<DataWeight> vec(first, last); |
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414 | std::sort(vec.begin(), vec.end()); |
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415 | init(vec, N); |
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416 | } |
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417 | |
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418 | |
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419 | }}} // end of namespace normalizer, yat and thep |
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420 | |
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421 | #endif |
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