[64] | 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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