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 | |
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9 | #include "defns.i" |
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10 | #include "types.i" |
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11 | #include "extern.i" |
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12 | |
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13 | |
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14 | ItemCount |
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15 | *Weight, /* Weight[i] = current fraction of item i */ |
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16 | **Freq, /* Freq[x][c] = no. items of class c with outcome x */ |
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17 | *ValFreq, /* ValFreq[x] = no. items with outcome x */ |
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18 | *ClassFreq; /* ClassFreq[c] = no. items of class c */ |
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19 | |
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20 | float |
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21 | *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 |
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27 | *Tested, /* Tested[a] set if att a has already been tested */ |
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28 | MultiVal; /* true when all atts have many values */ |
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29 | |
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30 | |
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31 | /* External variables initialised here */ |
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32 | |
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33 | extern float |
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34 | *SplitGain, /* SplitGain[i] = gain with att value of item i as threshold */ |
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35 | *SplitInfo; /* SplitInfo[i] = potential info ditto */ |
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36 | |
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37 | extern ItemCount |
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38 | *Slice1, /* Slice1[c] = saved values of Freq[x][c] in subset.c */ |
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39 | *Slice2; /* Slice2[c] = saved values of Freq[y][c] */ |
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40 | |
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41 | extern Set |
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42 | **Subset; /* Subset[a][s] = subset s for att a */ |
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43 | |
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44 | extern short |
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45 | *Subsets; /* Subsets[a] = no. subsets for att a */ |
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46 | |
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47 | |
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48 | |
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49 | /*************************************************************************/ |
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50 | /* */ |
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51 | /* Allocate space for tree tables */ |
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52 | /* */ |
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53 | /*************************************************************************/ |
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54 | |
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55 | |
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56 | InitialiseTreeData() |
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57 | /* ------------------ */ |
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58 | { |
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59 | DiscrValue v; |
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60 | Attribute a; |
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61 | |
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62 | Tested = (char *) calloc(MaxAtt+1, sizeof(char)); |
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63 | |
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64 | Gain = (float *) calloc(MaxAtt+1, sizeof(float)); |
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65 | Info = (float *) calloc(MaxAtt+1, sizeof(float)); |
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66 | Bar = (float *) calloc(MaxAtt+1, sizeof(float)); |
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67 | |
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68 | Subset = (Set **) calloc(MaxAtt+1, sizeof(Set *)); |
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69 | ForEach(a, 0, MaxAtt) |
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70 | { |
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71 | if ( MaxAttVal[a] ) |
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72 | { |
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73 | Subset[a] = (Set *) calloc(MaxDiscrVal+1, sizeof(Set)); |
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74 | ForEach(v, 0, MaxAttVal[a]) |
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75 | { |
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76 | Subset[a][v] = (Set) malloc((MaxAttVal[a]>>3) + 1); |
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77 | } |
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78 | } |
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79 | } |
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80 | Subsets = (short *) calloc(MaxAtt+1, sizeof(short)); |
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81 | |
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82 | SplitGain = (float *) calloc(MaxItem+1, sizeof(float)); |
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83 | SplitInfo = (float *) calloc(MaxItem+1, sizeof(float)); |
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84 | |
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85 | Weight = (ItemCount *) calloc(MaxItem+1, sizeof(ItemCount)); |
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86 | |
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87 | Freq = (ItemCount **) calloc(MaxDiscrVal+1, sizeof(ItemCount *)); |
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88 | ForEach(v, 0, MaxDiscrVal) |
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89 | { |
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90 | Freq[v] = (ItemCount *) calloc(MaxClass+1, sizeof(ItemCount)); |
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91 | } |
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92 | |
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93 | ValFreq = (ItemCount *) calloc(MaxDiscrVal+1, sizeof(ItemCount)); |
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94 | ClassFreq = (ItemCount *) calloc(MaxClass+1, sizeof(ItemCount)); |
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95 | |
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96 | Slice1 = (ItemCount *) calloc(MaxClass+2, sizeof(ItemCount)); |
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97 | Slice2 = (ItemCount *) calloc(MaxClass+2, sizeof(ItemCount)); |
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98 | |
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99 | UnknownRate = (float *) calloc(MaxAtt+1, sizeof(float)); |
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100 | |
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101 | /* Check whether all attributes have many discrete values */ |
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102 | |
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103 | MultiVal = true; |
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104 | if ( ! SUBSET ) |
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105 | { |
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106 | for ( a = 0 ; MultiVal && a <= MaxAtt ; a++ ) |
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107 | { |
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108 | if ( SpecialStatus[a] != IGNORE ) |
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109 | { |
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110 | MultiVal = MaxAttVal[a] >= 0.3 * (MaxItem + 1); |
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111 | } |
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112 | } |
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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 | /*************************************************************************/ |
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119 | /* */ |
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120 | /* Initialise the weight of each item */ |
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121 | /* */ |
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122 | /*************************************************************************/ |
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123 | |
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124 | |
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125 | InitialiseWeights() |
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126 | /* ----------------- */ |
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127 | { |
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128 | ItemNo i; |
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129 | |
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130 | ForEach(i, 0, MaxItem) |
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131 | { |
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132 | Weight[i] = 1.0; |
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133 | } |
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134 | } |
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135 | |
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136 | |
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137 | |
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138 | /*************************************************************************/ |
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139 | /* */ |
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140 | /* Build a decision tree for the cases Fp through Lp: */ |
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141 | /* */ |
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142 | /* - if all cases are of the same class, the tree is a leaf and so */ |
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143 | /* the leaf is returned labelled with this class */ |
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144 | /* */ |
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145 | /* - for each attribute, calculate the potential information provided */ |
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146 | /* by a test on the attribute (based on the probabilities of each */ |
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147 | /* case having a particular value for the attribute), and the gain */ |
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148 | /* in information that would result from a test on the attribute */ |
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149 | /* (based on the probabilities of each case with a particular */ |
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150 | /* value for the attribute being of a particular class) */ |
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151 | /* */ |
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152 | /* - on the basis of these figures, and depending on the current */ |
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153 | /* selection criterion, find the best attribute to branch on. */ |
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154 | /* Note: this version will not allow a split on an attribute */ |
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155 | /* unless two or more subsets have at least MINOBJS items. */ |
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156 | /* */ |
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157 | /* - try branching and test whether better than forming a leaf */ |
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158 | /* */ |
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159 | /*************************************************************************/ |
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160 | |
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161 | |
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162 | Tree FormTree(Fp, Lp) |
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163 | /* --------- */ |
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164 | ItemNo Fp, Lp; |
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165 | { |
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166 | ItemNo i, Kp, Ep, Group(); |
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167 | ItemCount Cases, NoBestClass, KnownCases, CountItems(); |
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168 | float Factor, BestVal, Val, AvGain=0, Worth(); |
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169 | Attribute Att, BestAtt, Possible=0; |
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170 | ClassNo c, BestClass; |
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171 | Tree Node, Leaf(); |
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172 | DiscrValue v; |
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173 | Boolean PrevAllKnown; |
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174 | |
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175 | Cases = CountItems(Fp, Lp); |
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176 | |
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177 | /* Generate the class frequency distribution */ |
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178 | |
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179 | ForEach(c, 0, MaxClass) |
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180 | { |
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181 | ClassFreq[c] = 0; |
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182 | } |
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183 | ForEach(i, Fp, Lp) |
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184 | { |
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185 | ClassFreq[ Class(Item[i]) ] += Weight[i]; |
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186 | } |
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187 | |
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188 | /* Find the most frequent class */ |
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189 | |
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190 | BestClass = 0; |
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191 | ForEach(c, 0, MaxClass) |
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192 | { |
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193 | if ( ClassFreq[c] > ClassFreq[BestClass] ) |
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194 | { |
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195 | BestClass = c; |
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196 | } |
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197 | } |
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198 | NoBestClass = ClassFreq[BestClass]; |
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199 | |
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200 | Node = Leaf(ClassFreq, BestClass, Cases, Cases - NoBestClass); |
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201 | |
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202 | /* If all cases are of the same class or there are not enough |
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203 | cases to divide, the tree is a leaf */ |
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204 | |
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205 | if ( NoBestClass == Cases || Cases < 2 * MINOBJS ) |
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206 | { |
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207 | return Node; |
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208 | } |
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209 | |
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210 | Verbosity(1) |
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211 | printf("\n%d items, total weight %.1f\n", Lp - Fp + 1, Cases); |
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212 | |
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213 | /* For each available attribute, find the information and gain */ |
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214 | |
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215 | ForEach(Att, 0, MaxAtt) |
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216 | { |
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217 | Gain[Att] = -Epsilon; |
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218 | |
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219 | if ( SpecialStatus[Att] == IGNORE ) continue; |
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220 | |
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221 | if ( MaxAttVal[Att] ) |
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222 | { |
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223 | /* discrete valued attribute */ |
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224 | |
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225 | if ( SUBSET && MaxAttVal[Att] > 2 ) |
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226 | { |
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227 | EvalSubset(Att, Fp, Lp, Cases); |
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228 | } |
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229 | else |
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230 | if ( ! Tested[Att] ) |
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231 | { |
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232 | EvalDiscreteAtt(Att, Fp, Lp, Cases); |
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233 | } |
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234 | } |
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235 | else |
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236 | { |
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237 | /* continuous attribute */ |
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238 | |
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239 | EvalContinuousAtt(Att, Fp, Lp); |
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240 | } |
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241 | |
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242 | /* Update average gain, excluding attributes with very many values */ |
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243 | |
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244 | if ( Gain[Att] > -Epsilon && |
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245 | ( MultiVal || MaxAttVal[Att] < 0.3 * (MaxItem + 1) ) ) |
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246 | { |
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247 | Possible++; |
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248 | AvGain += Gain[Att]; |
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249 | } |
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250 | } |
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251 | |
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252 | /* Find the best attribute according to the given criterion */ |
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253 | |
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254 | BestVal = -Epsilon; |
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255 | BestAtt = None; |
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256 | AvGain = ( Possible ? AvGain / Possible : 1E6 ); |
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257 | |
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258 | Verbosity(2) |
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259 | { |
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260 | if ( AvGain < 1E6 ) printf("\taverage gain %.3f\n", AvGain); |
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261 | } |
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262 | |
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263 | ForEach(Att, 0, MaxAtt) |
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264 | { |
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265 | if ( Gain[Att] > -Epsilon ) |
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266 | { |
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267 | Val = Worth(Info[Att], Gain[Att], AvGain); |
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268 | if ( Val > BestVal ) |
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269 | { |
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270 | BestAtt = Att; |
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271 | BestVal = Val; |
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272 | } |
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273 | } |
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274 | } |
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275 | |
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276 | /* Decide whether to branch or not */ |
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277 | |
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278 | if ( BestAtt != None ) |
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279 | { |
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280 | Verbosity(1) |
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281 | { |
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282 | printf("\tbest attribute %s", AttName[BestAtt]); |
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283 | if ( ! MaxAttVal[BestAtt] ) |
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284 | { |
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285 | printf(" cut %.3f", Bar[BestAtt]); |
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286 | } |
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287 | printf(" inf %.3f gain %.3f val %.3f\n", |
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288 | Info[BestAtt], Gain[BestAtt], BestVal); |
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289 | } |
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290 | |
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291 | /* Build a node of the selected test */ |
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292 | |
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293 | if ( MaxAttVal[BestAtt] ) |
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294 | { |
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295 | /* Discrete valued attribute */ |
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296 | |
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297 | if ( SUBSET && MaxAttVal[BestAtt] > 2 ) |
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298 | { |
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299 | SubsetTest(Node, BestAtt); |
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300 | } |
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301 | else |
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302 | { |
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303 | DiscreteTest(Node, BestAtt); |
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304 | } |
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305 | } |
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306 | else |
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307 | { |
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308 | /* Continuous attribute */ |
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309 | |
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310 | ContinTest(Node, BestAtt); |
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311 | } |
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312 | |
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313 | /* Remove unknown attribute values */ |
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314 | |
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315 | PrevAllKnown = AllKnown; |
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316 | |
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317 | Kp = Group(0, Fp, Lp, Node) + 1; |
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318 | if ( Kp != Fp ) AllKnown = false; |
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319 | KnownCases = Cases - CountItems(Fp, Kp-1); |
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320 | UnknownRate[BestAtt] = (Cases - KnownCases) / (Cases + 0.001); |
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321 | |
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322 | Verbosity(1) |
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323 | { |
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324 | if ( UnknownRate[BestAtt] > 0 ) |
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325 | { |
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326 | printf("\tunknown rate for %s = %.3f\n", |
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327 | AttName[BestAtt], UnknownRate[BestAtt]); |
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328 | } |
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329 | } |
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330 | |
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331 | /* Recursive divide and conquer */ |
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332 | |
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333 | ++Tested[BestAtt]; |
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334 | |
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335 | Ep = Kp - 1; |
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336 | Node->Errors = 0; |
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337 | |
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338 | ForEach(v, 1, Node->Forks) |
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339 | { |
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340 | Ep = Group(v, Kp, Lp, Node); |
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341 | |
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342 | if ( Kp <= Ep ) |
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343 | { |
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344 | Factor = CountItems(Kp, Ep) / KnownCases; |
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345 | |
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346 | ForEach(i, Fp, Kp-1) |
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347 | { |
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348 | Weight[i] *= Factor; |
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349 | } |
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350 | |
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351 | Node->Branch[v] = FormTree(Fp, Ep); |
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352 | Node->Errors += Node->Branch[v]->Errors; |
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353 | |
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354 | Group(0, Fp, Ep, Node); |
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355 | ForEach(i, Fp, Kp-1) |
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356 | { |
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357 | Weight[i] /= Factor; |
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358 | } |
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359 | } |
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360 | else |
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361 | { |
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362 | Node->Branch[v] = Leaf(Node->ClassDist, BestClass, 0.0, 0.0); |
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363 | } |
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364 | } |
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365 | |
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366 | --Tested[BestAtt]; |
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367 | AllKnown = PrevAllKnown; |
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368 | |
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369 | /* See whether we would have been no worse off with a leaf */ |
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370 | |
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371 | if ( Node->Errors >= Cases - NoBestClass - Epsilon ) |
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372 | { |
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373 | Verbosity(1) |
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374 | printf("Collapse tree for %d items to leaf %s\n", |
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375 | Lp - Fp + 1, ClassName[BestClass]); |
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376 | |
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377 | Node->NodeType = 0; |
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378 | } |
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379 | } |
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380 | else |
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381 | { |
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382 | Verbosity(1) |
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383 | printf("\tno sensible splits %.1f/%.1f\n", |
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384 | Cases, Cases - NoBestClass); |
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385 | } |
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386 | |
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387 | return Node; |
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388 | } |
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389 | |
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390 | |
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391 | |
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392 | /*************************************************************************/ |
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393 | /* */ |
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394 | /* Group together the items corresponding to branch V of a test */ |
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395 | /* and return the index of the last such */ |
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396 | /* */ |
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397 | /* Note: if V equals zero, group the unknown values */ |
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398 | /* */ |
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399 | /*************************************************************************/ |
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400 | |
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401 | |
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402 | ItemNo Group(V, Fp, Lp, TestNode) |
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403 | /* ----- */ |
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404 | DiscrValue V; |
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405 | ItemNo Fp, Lp; |
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406 | Tree TestNode; |
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407 | { |
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408 | ItemNo i; |
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409 | Attribute Att; |
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410 | float Thresh; |
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411 | Set SS; |
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412 | void Swap(); |
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413 | |
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414 | Att = TestNode->Tested; |
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415 | |
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416 | if ( V ) |
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417 | { |
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418 | /* Group items on the value of attribute Att, and depending |
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419 | on the type of branch */ |
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420 | |
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421 | switch ( TestNode->NodeType ) |
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422 | { |
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423 | case BrDiscr: |
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424 | |
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425 | ForEach(i, Fp, Lp) |
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426 | { |
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427 | if ( DVal(Item[i], Att) == V ) Swap(Fp++, i); |
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428 | } |
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429 | break; |
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430 | |
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431 | case ThreshContin: |
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432 | |
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433 | Thresh = TestNode->Cut; |
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434 | ForEach(i, Fp, Lp) |
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435 | { |
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436 | if ( (CVal(Item[i], Att) <= Thresh) == (V == 1) ) Swap(Fp++, i); |
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437 | } |
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438 | break; |
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439 | |
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440 | case BrSubset: |
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441 | |
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442 | SS = TestNode->Subset[V]; |
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443 | ForEach(i, Fp, Lp) |
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444 | { |
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445 | if ( In(DVal(Item[i], Att), SS) ) Swap(Fp++, i); |
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446 | } |
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447 | break; |
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448 | } |
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449 | } |
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450 | else |
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451 | { |
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452 | /* Group together unknown values */ |
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453 | |
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454 | switch ( TestNode->NodeType ) |
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455 | { |
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456 | case BrDiscr: |
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457 | case BrSubset: |
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458 | |
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459 | ForEach(i, Fp, Lp) |
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460 | { |
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461 | if ( ! DVal(Item[i], Att) ) Swap(Fp++, i); |
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462 | } |
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463 | break; |
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464 | |
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465 | case ThreshContin: |
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466 | |
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467 | ForEach(i, Fp, Lp) |
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468 | { |
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469 | if ( CVal(Item[i], Att) == Unknown ) Swap(Fp++, i); |
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470 | } |
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471 | break; |
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472 | } |
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473 | } |
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474 | |
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475 | return Fp - 1; |
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476 | } |
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477 | |
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478 | |
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479 | |
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480 | /*************************************************************************/ |
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481 | /* */ |
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482 | /* Return the total weight of items from Fp to Lp */ |
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483 | /* */ |
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484 | /*************************************************************************/ |
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485 | |
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486 | |
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487 | ItemCount CountItems(Fp, Lp) |
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488 | /* ---------- */ |
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489 | ItemNo Fp, Lp; |
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490 | { |
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491 | register ItemCount Sum=0.0, *Wt, *LWt; |
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492 | |
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493 | if ( AllKnown ) return Lp - Fp + 1; |
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494 | |
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495 | for ( Wt = Weight + Fp, LWt = Weight + Lp ; Wt <= LWt ; ) |
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496 | { |
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497 | Sum += *Wt++; |
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498 | } |
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499 | |
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500 | return Sum; |
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501 | } |
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502 | |
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503 | |
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504 | |
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505 | /*************************************************************************/ |
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506 | /* */ |
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507 | /* Exchange items at a and b */ |
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508 | /* */ |
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509 | /*************************************************************************/ |
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510 | |
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511 | |
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512 | void Swap(a,b) |
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513 | /* ---- */ |
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514 | ItemNo a, b; |
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515 | { |
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516 | register Description Hold; |
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517 | register ItemCount HoldW; |
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518 | |
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519 | Hold = Item[a]; |
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520 | Item[a] = Item[b]; |
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521 | Item[b] = Hold; |
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522 | |
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523 | HoldW = Weight[a]; |
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524 | Weight[a] = Weight[b]; |
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525 | Weight[b] = HoldW; |
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526 | } |
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