1 | /*************************************************************************/ |
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2 | /* */ |
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3 | /* Central tree-forming algorithm incorporating all criteria */ |
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4 | /* --------------------------------------------------------- */ |
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5 | /* */ |
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6 | /*************************************************************************/ |
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7 | |
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8 | #include "defns.i" |
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9 | #include "types.i" |
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10 | #include "extern.i" |
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11 | |
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12 | |
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13 | #include <omp.h> |
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14 | |
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15 | |
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16 | ItemCount *Weight, /* Weight[i] = current fraction of item i */ |
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17 | **Freq, /* Freq[x][c] = no. items of class c with outcome x */ |
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18 | *ValFreq, /* ValFreq[x] = no. items with outcome x */ |
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19 | *ClassFreq; /* ClassFreq[c] = no. items of class c */ |
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20 | |
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21 | float *Gain, /* Gain[a] = info gain by split on att a */ |
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22 | *Info, /* Info[a] = potential info of split on att a */ |
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23 | *Bar, /* Bar[a] = best threshold for contin att a */ |
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24 | *UnknownRate; /* UnknownRate[a] = current unknown rate for att a */ |
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25 | |
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26 | Boolean *Tested, /* Tested[a] set if att a has already been tested */ |
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27 | MultiVal; /* true when all atts have many values */ |
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28 | |
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29 | /* External variables initialised here */ |
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30 | |
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31 | extern float *SplitGain, /* SplitGain[i] = gain with att value of item i as threshold */ |
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32 | *SplitInfo; /* SplitInfo[i] = potential info ditto */ |
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33 | |
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34 | extern ItemCount *Slice1, /* Slice1[c] = saved values of Freq[x][c] in subset.c */ |
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35 | *Slice2; /* Slice2[c] = saved values of Freq[y][c] */ |
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36 | |
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37 | extern Set **Subset; /* Subset[a][s] = subset s for att a */ |
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38 | |
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39 | extern short *Subsets; /* Subsets[a] = no. subsets for att a */ |
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40 | |
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41 | /*************************************************************************/ |
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42 | /* */ |
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43 | /* Allocate space for tree tables */ |
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44 | /* */ |
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45 | /*************************************************************************/ |
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46 | |
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47 | InitialiseTreeData() |
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48 | /* ------------------ */ |
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49 | { |
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50 | DiscrValue v; |
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51 | Attribute a; |
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52 | |
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53 | Tested = (char *) calloc(MaxAtt + 1, sizeof(char)); |
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54 | |
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55 | Gain = (float *) calloc(MaxAtt + 1, sizeof(float)); |
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56 | Info = (float *) calloc(MaxAtt + 1, sizeof(float)); |
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57 | Bar = (float *) calloc(MaxAtt + 1, sizeof(float)); |
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58 | |
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59 | Subset = (Set **) calloc(MaxAtt + 1, sizeof(Set *)); |
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60 | ForEach(a, 0, MaxAtt) { |
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61 | if (MaxAttVal[a]) { |
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62 | Subset[a] = (Set *) calloc(MaxDiscrVal + 1, sizeof(Set)); |
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63 | ForEach(v, 0, MaxAttVal[a]) { |
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64 | Subset[a][v] = (Set) malloc((MaxAttVal[a] >> 3) + 1); |
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65 | } |
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66 | } |
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67 | } |
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68 | Subsets = (short *) calloc(MaxAtt + 1, sizeof(short)); |
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69 | |
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70 | SplitGain = (float *) calloc(MaxItem + 1, sizeof(float)); |
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71 | SplitInfo = (float *) calloc(MaxItem + 1, sizeof(float)); |
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72 | |
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73 | Weight = (ItemCount *) calloc(MaxItem + 1, sizeof(ItemCount)); |
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74 | |
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75 | Freq = (ItemCount **) calloc(MaxDiscrVal + 1, sizeof(ItemCount *)); |
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76 | ForEach(v, 0, MaxDiscrVal) { |
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77 | Freq[v] = (ItemCount *) calloc(MaxClass + 1, sizeof(ItemCount)); |
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78 | } |
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79 | |
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80 | ValFreq = (ItemCount *) calloc(MaxDiscrVal + 1, sizeof(ItemCount)); |
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81 | ClassFreq = (ItemCount *) calloc(MaxClass + 1, sizeof(ItemCount)); |
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82 | |
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83 | Slice1 = (ItemCount *) calloc(MaxClass + 2, sizeof(ItemCount)); |
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84 | Slice2 = (ItemCount *) calloc(MaxClass + 2, sizeof(ItemCount)); |
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85 | |
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86 | UnknownRate = (float *) calloc(MaxAtt + 1, sizeof(float)); |
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87 | |
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88 | /* Check whether all attributes have many discrete values */ |
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89 | |
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90 | MultiVal = true; |
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91 | if (!SUBSET) { |
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92 | for (a = 0; MultiVal && a <= MaxAtt; a++) { |
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93 | if (SpecialStatus[a] != IGNORE) { |
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94 | MultiVal = MaxAttVal[a] >= 0.3 * (MaxItem + 1); |
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95 | } |
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96 | } |
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97 | } |
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98 | } |
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99 | |
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100 | /*************************************************************************/ |
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101 | /* */ |
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102 | /* Initialise the weight of each item */ |
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103 | /* */ |
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104 | /*************************************************************************/ |
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105 | |
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106 | InitialiseWeights() |
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107 | /* ----------------- */ |
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108 | { |
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109 | ItemNo i; |
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110 | |
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111 | ForEach(i, 0, MaxItem) { |
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112 | Weight[i] = 1.0; |
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113 | } |
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114 | } |
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115 | |
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116 | /*************************************************************************/ |
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117 | /* */ |
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118 | /* Build a decision tree for the cases Fp through Lp: */ |
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119 | /* */ |
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120 | /* - if all cases are of the same class, the tree is a leaf and so */ |
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121 | /* the leaf is returned labelled with this class */ |
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122 | /* */ |
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123 | /* - for each attribute, calculate the potential information provided */ |
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124 | /* by a test on the attribute (based on the probabilities of each */ |
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125 | /* case having a particular value for the attribute), and the gain */ |
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126 | /* in information that would result from a test on the attribute */ |
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127 | /* (based on the probabilities of each case with a particular */ |
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128 | /* value for the attribute being of a particular class) */ |
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129 | /* */ |
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130 | /* - on the basis of these figures, and depending on the current */ |
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131 | /* selection criterion, find the best attribute to branch on. */ |
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132 | /* Note: this version will not allow a split on an attribute */ |
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133 | /* unless two or more subsets have at least MINOBJS items. */ |
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134 | /* */ |
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135 | /* - try branching and test whether better than forming a leaf */ |
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136 | /* */ |
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137 | /*************************************************************************/ |
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138 | |
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139 | Tree FormTree(Fp, Lp) |
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140 | /* --------- */ |
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141 | ItemNo Fp, Lp; { |
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142 | ItemNo i, Kp, Ep, Group(); |
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143 | ItemCount Cases, NoBestClass, KnownCases, CountItems(); |
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144 | float Factor, BestVal, Val, AvGain = 0, Worth(); |
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145 | Attribute Att, BestAtt, Possible = 0; |
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146 | ClassNo c, BestClass; |
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147 | Tree Node, Leaf(); |
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148 | DiscrValue v; |
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149 | Boolean PrevAllKnown; |
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150 | |
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151 | Cases = CountItems(Fp, Lp); |
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152 | |
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153 | /* Generate the class frequency distribution */ |
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154 | |
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155 | //printf("The parallel region is executed by thread %d\n", omp_get_thread_num()); |
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156 | |
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157 | /* THIS CAN BE PARALELIZED */ |
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158 | ForEach(c, 0, MaxClass) { |
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159 | ClassFreq[c] = 0; |
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160 | } |
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161 | |
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162 | /* THIS CAN BE PARALELIZED */ |
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163 | ForEach(i, Fp, Lp) { |
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164 | ClassFreq[Class(Item[i])] += Weight[i]; |
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165 | } |
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166 | |
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167 | /* Find the most frequent class */ |
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168 | /* THIS CAN BE PARALELIZED */ |
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169 | BestClass = 0; |
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170 | |
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171 | ForEach(c, 0, MaxClass) { |
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172 | if (ClassFreq[c] > ClassFreq[BestClass]) { |
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173 | BestClass = c; |
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174 | } |
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175 | } |
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176 | |
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177 | NoBestClass = ClassFreq[BestClass]; |
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178 | |
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179 | Node = Leaf(ClassFreq, BestClass, Cases, Cases - NoBestClass); |
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180 | |
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181 | /* If all cases are of the same class or there are not enough |
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182 | cases to divide, the tree is a leaf */ |
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183 | |
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184 | if (NoBestClass == Cases || Cases < 2 * MINOBJS) { |
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185 | return Node; |
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186 | } |
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187 | |
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188 | Verbosity(1) |
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189 | printf("\n%d items, total weight %.1f\n", Lp - Fp + 1, Cases); |
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190 | |
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191 | /* For each available attribute, find the information and gain */ |
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192 | /* THIS MUST BE PARALELIZED */ |
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193 | |
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194 | ForEach(Att, 0, MaxAtt) { |
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195 | Gain[Att] = -Epsilon; |
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196 | |
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197 | if (SpecialStatus[Att] == IGNORE) |
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198 | continue; |
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199 | |
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200 | if (MaxAttVal[Att]) { |
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201 | /* discrete valued attribute */ |
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202 | |
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203 | if (SUBSET && MaxAttVal[Att] > 2) { |
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204 | EvalSubset(Att, Fp, Lp, Cases); |
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205 | } else if (!Tested[Att]) { |
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206 | EvalDiscreteAtt(Att, Fp, Lp, Cases); |
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207 | } |
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208 | } else { |
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209 | /* continuous attribute */ |
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210 | |
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211 | EvalContinuousAtt(Att, Fp, Lp); |
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212 | } |
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213 | |
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214 | /* Update average gain, excluding attributes with very many values */ |
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215 | |
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216 | if (Gain[Att] > -Epsilon && (MultiVal || MaxAttVal[Att] < 0.3 |
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217 | * (MaxItem + 1))) { |
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218 | Possible++; |
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219 | AvGain += Gain[Att]; |
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220 | } |
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221 | } |
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222 | |
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223 | /* Find the best attribute according to the given criterion */ |
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224 | |
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225 | BestVal = -Epsilon; |
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226 | BestAtt = None; |
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227 | AvGain = (Possible ? AvGain / Possible : 1E6); |
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228 | |
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229 | Verbosity(2) { |
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230 | if (AvGain < 1E6) |
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231 | printf("\taverage gain %.3f\n", AvGain); |
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232 | } |
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233 | |
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234 | ForEach(Att, 0, MaxAtt) { |
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235 | if (Gain[Att] > -Epsilon) { |
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236 | Val = Worth(Info[Att], Gain[Att], AvGain); |
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237 | if (Val > BestVal) { |
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238 | BestAtt = Att; |
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239 | BestVal = Val; |
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240 | } |
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241 | } |
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242 | } |
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243 | |
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244 | /* Decide whether to branch or not */ |
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245 | |
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246 | if (BestAtt != None) { |
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247 | Verbosity(1) { |
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248 | printf("\tbest attribute %s", AttName[BestAtt]); |
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249 | if (!MaxAttVal[BestAtt]) { |
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250 | printf(" cut %.3f", Bar[BestAtt]); |
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251 | } |
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252 | printf(" inf %.3f gain %.3f val %.3f\n", Info[BestAtt], |
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253 | Gain[BestAtt], BestVal); |
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254 | } |
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255 | |
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256 | /* Build a node of the selected test */ |
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257 | |
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258 | if (MaxAttVal[BestAtt]) { |
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259 | /* Discrete valued attribute */ |
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260 | |
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261 | if (SUBSET && MaxAttVal[BestAtt] > 2) { |
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262 | SubsetTest(Node, BestAtt); |
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263 | } else { |
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264 | DiscreteTest(Node, BestAtt); |
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265 | } |
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266 | } else { |
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267 | /* Continuous attribute */ |
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268 | |
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269 | ContinTest(Node, BestAtt); |
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270 | } |
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271 | |
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272 | /* Remove unknown attribute values */ |
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273 | |
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274 | PrevAllKnown = AllKnown; |
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275 | |
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276 | Kp = Group(0, Fp, Lp, Node) + 1; |
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277 | if (Kp != Fp) |
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278 | AllKnown = false; |
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279 | KnownCases = Cases - CountItems(Fp, Kp - 1); |
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280 | UnknownRate[BestAtt] = (Cases - KnownCases) / (Cases + 0.001); |
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281 | |
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282 | Verbosity(1) { |
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283 | if (UnknownRate[BestAtt] > 0) { |
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284 | printf("\tunknown rate for %s = %.3f\n", AttName[BestAtt], |
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285 | UnknownRate[BestAtt]); |
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286 | } |
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287 | } |
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288 | |
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289 | /* Recursive divide and conquer */ |
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290 | |
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291 | ++Tested[BestAtt]; |
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292 | |
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293 | Ep = Kp - 1; |
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294 | Node->Errors = 0; |
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295 | |
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296 | ForEach(v, 1, Node->Forks) { |
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297 | Ep = Group(v, Kp, Lp, Node); |
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298 | |
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299 | if (Kp <= Ep) { |
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300 | Factor = CountItems(Kp, Ep) / KnownCases; |
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301 | |
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302 | ForEach(i, Fp, Kp-1) { |
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303 | Weight[i] *= Factor; |
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304 | } |
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305 | |
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306 | #pragma omp task untied default(shared) |
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307 | { |
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308 | Node->Branch[v] = FormTree(Fp, Ep); |
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309 | } |
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310 | |
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311 | #pragma omp taskwait |
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312 | Node->Errors += Node->Branch[v]->Errors; |
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313 | |
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314 | Group(0, Fp, Ep, Node); |
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315 | ForEach(i, Fp, Kp-1) { |
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316 | Weight[i] /= Factor; |
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317 | } |
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318 | } else { |
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319 | Node->Branch[v] = Leaf(Node->ClassDist, BestClass, 0.0, 0.0); |
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320 | } |
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321 | } |
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322 | |
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323 | --Tested[BestAtt]; |
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324 | AllKnown = PrevAllKnown; |
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325 | |
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326 | /* See whether we would have been no worse off with a leaf */ |
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327 | |
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328 | if (Node->Errors >= Cases - NoBestClass - Epsilon) { |
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329 | Verbosity(1) |
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330 | printf("Collapse tree for %d items to leaf %s\n", Lp - Fp + 1, |
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331 | ClassName[BestClass]); |
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332 | |
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333 | Node->NodeType = 0; |
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334 | } |
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335 | } else { |
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336 | Verbosity(1) |
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337 | printf("\tno sensible splits %.1f/%.1f\n", Cases, Cases |
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338 | - NoBestClass); |
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339 | } |
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340 | |
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341 | return Node; |
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342 | } |
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343 | |
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344 | /*************************************************************************/ |
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345 | /* */ |
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346 | /* Group together the items corresponding to branch V of a test */ |
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347 | /* and return the index of the last such */ |
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348 | /* */ |
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349 | /* Note: if V equals zero, group the unknown values */ |
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350 | /* */ |
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351 | /*************************************************************************/ |
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352 | |
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353 | ItemNo Group(V, Fp, Lp, TestNode) |
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354 | /* ----- */ |
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355 | DiscrValue V;ItemNo Fp, Lp;Tree TestNode; { |
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356 | ItemNo i; |
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357 | Attribute Att; |
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358 | float Thresh; |
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359 | Set SS; |
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360 | void Swap(); |
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361 | |
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362 | Att = TestNode->Tested; |
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363 | |
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364 | if (V) { |
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365 | /* Group items on the value of attribute Att, and depending |
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366 | on the type of branch */ |
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367 | |
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368 | switch (TestNode->NodeType) { |
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369 | case BrDiscr: |
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370 | |
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371 | ForEach(i, Fp, Lp) { |
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372 | if (DVal(Item[i], Att) == V) |
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373 | Swap(Fp++, i); |
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374 | } |
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375 | break; |
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376 | |
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377 | case ThreshContin: |
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378 | |
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379 | Thresh = TestNode->Cut; |
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380 | ForEach(i, Fp, Lp) { |
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381 | if ((CVal(Item[i], Att) <= Thresh) == (V == 1)) |
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382 | Swap(Fp++, i); |
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383 | } |
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384 | break; |
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385 | |
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386 | case BrSubset: |
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387 | |
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388 | SS = TestNode->Subset[V]; |
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389 | ForEach(i, Fp, Lp) { |
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390 | if (In(DVal(Item[i], Att), SS)) |
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391 | Swap(Fp++, i); |
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392 | } |
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393 | break; |
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394 | } |
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395 | } else { |
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396 | /* Group together unknown values */ |
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397 | |
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398 | switch (TestNode->NodeType) { |
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399 | case BrDiscr: |
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400 | case BrSubset: |
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401 | |
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402 | ForEach(i, Fp, Lp) { |
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403 | if (!DVal(Item[i], Att)) |
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404 | Swap(Fp++, i); |
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405 | } |
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406 | break; |
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407 | |
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408 | case ThreshContin: |
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409 | |
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410 | ForEach(i, Fp, Lp) { |
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411 | if (CVal(Item[i], Att) == Unknown) |
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412 | Swap(Fp++, i); |
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413 | } |
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414 | break; |
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415 | } |
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416 | } |
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417 | |
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418 | return Fp - 1; |
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419 | } |
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420 | |
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421 | /*************************************************************************/ |
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422 | /* */ |
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423 | /* Return the total weight of items from Fp to Lp */ |
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424 | /* */ |
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425 | /*************************************************************************/ |
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426 | |
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427 | ItemCount CountItems(Fp, Lp) |
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428 | /* ---------- */ |
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429 | ItemNo Fp, Lp; { |
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430 | register ItemCount Sum = 0.0, *Wt, *LWt; |
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431 | |
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432 | if (AllKnown) |
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433 | return Lp - Fp + 1; |
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434 | |
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435 | for (Wt = Weight + Fp, LWt = Weight + Lp; Wt <= LWt;) { |
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436 | Sum += *Wt++; |
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437 | } |
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438 | |
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439 | return Sum; |
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440 | } |
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441 | |
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442 | /*************************************************************************/ |
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443 | /* */ |
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444 | /* Exchange items at a and b */ |
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445 | /* */ |
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446 | /*************************************************************************/ |
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447 | |
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448 | void Swap(a, b) |
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449 | /* ---- */ |
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450 | ItemNo a, b; { |
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451 | register Description Hold; |
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452 | register ItemCount HoldW; |
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453 | |
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454 | Hold = Item[a]; |
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455 | Item[a] = Item[b]; |
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456 | Item[b] = Hold; |
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457 | |
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458 | HoldW = Weight[a]; |
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459 | Weight[a] = Weight[b]; |
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460 | Weight[b] = HoldW; |
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461 | } |
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