[24] | 1 | /*************************************************************************/ |
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| 2 | /* */ |
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| 3 | /* Evaluation of the subsetting of a discrete attribute */ |
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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 "buildex.i" |
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| 10 | |
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| 11 | |
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| 12 | ItemCount |
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| 13 | *Slice1, /* Slice1[c] = saved values of Freq[x][c] in subset.c */ |
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| 14 | *Slice2; /* Slice2[c] = saved values of Freq[y][c] */ |
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| 15 | |
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| 16 | Set |
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| 17 | **Subset; /* Subset[a][s] = subset s for att a */ |
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| 18 | |
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| 19 | short |
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| 20 | *Subsets; /* Subsets[a] = no. subsets for att a */ |
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| 21 | |
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| 22 | |
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| 23 | |
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| 24 | /*************************************************************************/ |
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| 25 | /* */ |
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| 26 | /* Evaluate subsetting a discrete attribute and form the chosen */ |
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| 27 | /* subsets Subset[Att][], setting Subsets[Att] to the number of */ |
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| 28 | /* subsets, and the Info[] and Gain[] of a test on the attribute */ |
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| 29 | /* */ |
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| 30 | /*************************************************************************/ |
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| 31 | |
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| 32 | |
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| 33 | EvalSubset(Att, Fp, Lp, Items) |
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| 34 | /* ---------- */ |
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| 35 | Attribute Att; |
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| 36 | ItemNo Fp, Lp; |
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| 37 | ItemCount Items; |
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| 38 | { |
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| 39 | DiscrValue V1, V2, BestV1, BestV2, Barred; |
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| 40 | ItemCount KnownItems; |
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| 41 | ClassNo c; |
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| 42 | float BaseInfo, MinGain, ThisGain, ThisInfo, |
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| 43 | Val, BestVal, BestGain, BestInfo, |
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| 44 | PrevVal, PrevGain, PrevInfo, |
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| 45 | DiscrKnownBaseInfo(), Worth(), ComputeGain(), TotalInfo(); |
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| 46 | short Blocks=0, MissingValues=0, ReasonableSubsets, Bytes, b; |
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| 47 | Boolean MergedSubsets = false; |
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| 48 | int SaveMINOBJS; |
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| 49 | |
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| 50 | SaveMINOBJS = MINOBJS; |
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| 51 | MINOBJS = 1; |
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| 52 | |
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| 53 | /* First compute Freq[][], ValFreq[], base info, and the gain |
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| 54 | and total info of a split on discrete attribute Att */ |
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| 55 | |
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| 56 | ComputeFrequencies(Att, Fp, Lp); |
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| 57 | |
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| 58 | KnownItems = Items - ValFreq[0]; |
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| 59 | if ( KnownItems < Epsilon ) |
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| 60 | { |
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| 61 | Verbosity(2) printf("\tAtt %s: no known values\n", AttName[Att]); |
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| 62 | |
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| 63 | Gain[Att] = -Epsilon; |
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| 64 | Info[Att] = 0; |
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| 65 | return; |
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| 66 | } |
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| 67 | |
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| 68 | BaseInfo = DiscrKnownBaseInfo(KnownItems, MaxAttVal[Att]); |
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| 69 | |
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| 70 | PrevGain = ComputeGain(BaseInfo, UnknownRate[Att], MaxAttVal[Att],KnownItems); |
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| 71 | PrevInfo = TotalInfo(ValFreq, 0, MaxAttVal[Att]) / Items; |
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| 72 | PrevVal = Worth(PrevInfo, PrevGain, Epsilon); |
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| 73 | |
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| 74 | Verbosity(2) |
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| 75 | { |
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| 76 | printf("\tAtt %s", AttName[Att]); |
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| 77 | |
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| 78 | Verbosity(3) PrintDistribution(Att, MaxAttVal[Att], true); |
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| 79 | |
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| 80 | printf("\tinf %.3f, gain %.3f, val=%.3f\n", |
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| 81 | PrevInfo, PrevGain, PrevVal); |
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| 82 | } |
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| 83 | |
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| 84 | /* Eliminate unrepresented attribute values from Freq[] and ValFreq[] |
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| 85 | and form a separate subset for each represented attribute value */ |
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| 86 | |
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| 87 | Bytes = (MaxAttVal[Att]>>3) + 1; |
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| 88 | ClearBits(Bytes, Subset[Att][0]); |
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| 89 | |
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| 90 | ForEach(V1, 1, MaxAttVal[Att]) |
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| 91 | { |
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| 92 | if ( ValFreq[V1] > 0.5 ) |
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| 93 | { |
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| 94 | if ( ++Blocks < V1 ) |
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| 95 | { |
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| 96 | ValFreq[Blocks] = ValFreq[V1]; |
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| 97 | ForEach(c, 0, MaxClass) |
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| 98 | { |
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| 99 | Freq[Blocks][c] = Freq[V1][c]; |
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| 100 | } |
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| 101 | } |
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| 102 | ClearBits(Bytes, Subset[Att][Blocks]); |
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| 103 | SetBit(V1, Subset[Att][Blocks]); |
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| 104 | } |
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| 105 | else |
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| 106 | { |
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| 107 | SetBit(V1, Subset[Att][0]); |
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| 108 | MissingValues++; |
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| 109 | } |
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| 110 | } |
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| 111 | |
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| 112 | /* Merge any single-class subsets with others of the same class */ |
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| 113 | /* Note: have ValFreq[V] > 0 for all V */ |
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| 114 | |
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| 115 | ForEach(V1, 1, Blocks-1) |
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| 116 | { |
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| 117 | for ( c = 0 ; Freq[V1][c] < 0.1 ; c++ ) |
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| 118 | ; |
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| 119 | |
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| 120 | if ( Freq[V1][c] < ValFreq[V1] - 0.1 ) continue; |
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| 121 | |
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| 122 | /* Now have a single class -- look for others */ |
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| 123 | |
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| 124 | for ( V2 = V1+1 ; V2 <= Blocks ; ) |
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| 125 | { |
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| 126 | if ( Freq[V2][c] < ValFreq[V2] - 0.1 ) |
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| 127 | { |
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| 128 | V2++; |
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| 129 | } |
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| 130 | else |
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| 131 | { |
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| 132 | /* Merge these subsets */ |
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| 133 | |
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| 134 | Combine(V1, V2, Blocks); |
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| 135 | |
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| 136 | ForEach(b, 0, Bytes-1) |
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| 137 | { |
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| 138 | Subset[Att][V1][b] |= Subset[Att][V2][b]; |
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| 139 | Subset[Att][V2][b] = Subset[Att][Blocks][b]; |
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| 140 | } |
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| 141 | |
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| 142 | Blocks--; |
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| 143 | MergedSubsets = true; |
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| 144 | } |
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| 145 | } |
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| 146 | } |
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| 147 | |
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| 148 | if ( MergedSubsets ) |
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| 149 | { |
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| 150 | PrevGain = ComputeGain(BaseInfo, UnknownRate[Att], Blocks, KnownItems); |
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| 151 | PrevInfo = TotalInfo(ValFreq, 0, Blocks) / Items; |
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| 152 | PrevVal = Worth(PrevInfo, PrevGain, Epsilon); |
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| 153 | |
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| 154 | Verbosity(2) |
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| 155 | { |
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| 156 | printf("\tAfter merging single-class subsets:"); |
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| 157 | |
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| 158 | Verbosity(3) PrintDistribution(Att, Blocks, false); |
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| 159 | |
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| 160 | printf("\tinf %.3f, gain %.3f, val=%.3f\n", |
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| 161 | PrevInfo, PrevGain, PrevVal); |
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| 162 | } |
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| 163 | } |
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| 164 | |
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| 165 | /* Examine possible pair mergers and hill-climb */ |
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| 166 | |
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| 167 | MinGain = PrevGain / 2; |
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| 168 | |
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| 169 | while ( Blocks > 2 ) |
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| 170 | { |
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| 171 | BestVal = BestV1 = 0; |
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| 172 | BestGain = -Epsilon; |
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| 173 | |
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| 174 | /* Check reasonable subsets; if less than 3, bar mergers |
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| 175 | involving the largest block */ |
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| 176 | |
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| 177 | ReasonableSubsets = 0; |
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| 178 | Barred = 1; |
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| 179 | |
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| 180 | ForEach(V1, 1, Blocks) |
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| 181 | { |
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| 182 | if ( ValFreq[V1] >= SaveMINOBJS ) ReasonableSubsets++; |
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| 183 | |
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| 184 | if ( ValFreq[V1] > ValFreq[Barred] ) Barred = V1; |
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| 185 | } |
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| 186 | |
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| 187 | if ( ReasonableSubsets >= 3 ) Barred = 0; |
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| 188 | |
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| 189 | /* For each possible pair of values, calculate the gain and |
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| 190 | total info of a split in which they are treated as one. |
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| 191 | Keep track of the pair with the best gain. */ |
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| 192 | |
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| 193 | ForEach(V1, 1, Blocks-1) |
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| 194 | { |
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| 195 | ForEach(V2, V1+1, Blocks) |
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| 196 | { |
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| 197 | if ( V1 == Barred || V2 == Barred ) continue; |
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| 198 | |
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| 199 | Combine(V1, V2, Blocks); |
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| 200 | |
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| 201 | ThisGain = ComputeGain(BaseInfo, UnknownRate[Att], |
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| 202 | Blocks-1, KnownItems); |
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| 203 | ThisInfo = TotalInfo(ValFreq, 0, Blocks-1) / Items; |
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| 204 | Val = Worth(ThisInfo, ThisGain, Epsilon); |
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| 205 | |
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| 206 | Verbosity(4) |
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| 207 | { |
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| 208 | printf("\tcombine %d %d info %.3f gain %.3f val %.3f", |
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| 209 | V1, V2, ThisInfo, ThisGain, Val); |
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| 210 | PrintDistribution(Att, Blocks-1, false); |
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| 211 | } |
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| 212 | |
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| 213 | /* Force a split if |
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| 214 | less than two reasonable subsets, or |
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| 215 | using GAIN criterion |
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| 216 | Prefer this split to the previous one if |
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| 217 | gain >= MinGain (and previous < MinGain), or |
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| 218 | val >= previous best val */ |
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| 219 | |
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| 220 | if ( ThisGain >= MinGain && BestGain < MinGain || |
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| 221 | Val >= BestVal || |
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| 222 | ! BestV1 && ( ! GAINRATIO || ReasonableSubsets < 2 ) ) |
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| 223 | { |
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| 224 | BestVal = Val; |
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| 225 | BestGain = ThisGain; |
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| 226 | BestInfo = ThisInfo; |
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| 227 | BestV1 = V1; |
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| 228 | BestV2 = V2; |
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| 229 | } |
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| 230 | |
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| 231 | Uncombine(V1, V2); |
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| 232 | } |
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| 233 | } |
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| 234 | |
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| 235 | if ( GAINRATIO && |
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| 236 | ReasonableSubsets >= 2 && |
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| 237 | ( ! BestV1 || |
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| 238 | BestVal < PrevVal + 1E-5 || |
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| 239 | BestVal == PrevVal && BestGain < PrevGain ) ) break; |
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| 240 | |
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| 241 | PrevGain = BestGain; |
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| 242 | PrevInfo = BestInfo; |
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| 243 | PrevVal = BestVal; |
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| 244 | |
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| 245 | Combine(BestV1, BestV2, Blocks); |
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| 246 | |
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| 247 | ForEach(b, 0, Bytes-1) |
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| 248 | { |
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| 249 | Subset[Att][BestV1][b] |= Subset[Att][BestV2][b]; |
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| 250 | Subset[Att][BestV2][b] = Subset[Att][Blocks][b]; |
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| 251 | } |
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| 252 | |
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| 253 | Blocks--; |
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| 254 | |
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| 255 | Verbosity(2) |
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| 256 | { |
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| 257 | printf("\t\tform subset "); |
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| 258 | PrintSubset(Att, Subset[Att][BestV1]); |
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| 259 | printf(": %d subsets, inf %.3f, gain %.3f, val %.3f\n", |
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| 260 | Blocks, BestInfo, BestGain, BestVal); |
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| 261 | Verbosity(3) |
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| 262 | { |
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| 263 | printf("\t\tcombine %d, %d", BestV1, BestV2); |
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| 264 | PrintDistribution(Att, Blocks, false); |
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| 265 | } |
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| 266 | } |
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| 267 | } |
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| 268 | |
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| 269 | MINOBJS = SaveMINOBJS; |
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| 270 | |
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| 271 | if ( PrevVal <= 0 ) |
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| 272 | { |
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| 273 | Gain[Att] = -Epsilon; |
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| 274 | Info[Att] = 0; |
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| 275 | } |
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| 276 | else |
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| 277 | { |
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| 278 | Gain[Att] = ComputeGain(BaseInfo, UnknownRate[Att], Blocks, KnownItems); |
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| 279 | Info[Att] = PrevInfo; |
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| 280 | |
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| 281 | if ( MissingValues ) |
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| 282 | { |
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| 283 | Blocks++; |
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| 284 | CopyBits(Bytes, Subset[Att][0], Subset[Att][Blocks]); |
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| 285 | } |
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| 286 | |
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| 287 | Subsets[Att] = Blocks; |
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| 288 | |
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| 289 | Verbosity(2) printf("\tFinal subsets:"); |
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| 290 | Verbosity(3) PrintDistribution(Att, Blocks, false); |
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| 291 | Verbosity(2) |
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| 292 | printf("\tinf %.3f gain %.3f val %.3f\n", |
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| 293 | Info[Att], Gain[Att], Worth(Info[Att], Gain[Att], Epsilon)); |
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| 294 | } |
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| 295 | } |
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| 296 | |
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| 297 | |
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| 298 | |
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| 299 | /*************************************************************************/ |
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| 300 | /* */ |
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| 301 | /* Combine the distribution figures of discrete attribute values */ |
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| 302 | /* x and y, putting the combined figures in Freq[x][] and */ |
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| 303 | /* ValFreq[x][], and saving old values in Slice1 and Slice2 */ |
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| 304 | /* */ |
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| 305 | /*************************************************************************/ |
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| 306 | |
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| 307 | |
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| 308 | Combine(x, y, Last) |
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| 309 | /* ------- */ |
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| 310 | DiscrValue x, y, Last; |
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| 311 | { |
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| 312 | ClassNo c; |
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| 313 | |
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| 314 | ForEach(c, 0, MaxClass) |
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| 315 | { |
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| 316 | Slice1[c] = Freq[x][c]; |
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| 317 | Slice2[c] = Freq[y][c]; |
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| 318 | |
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| 319 | Freq[x][c] += Freq[y][c]; |
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| 320 | Freq[y][c] = Freq[Last][c]; |
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| 321 | } |
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| 322 | |
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| 323 | Slice1[MaxClass+1] = ValFreq[x]; |
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| 324 | Slice2[MaxClass+1] = ValFreq[y]; |
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| 325 | |
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| 326 | ValFreq[x] += ValFreq[y]; |
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| 327 | ValFreq[y] = ValFreq[Last]; |
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| 328 | } |
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| 329 | |
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| 330 | |
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| 331 | |
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| 332 | /*************************************************************************/ |
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| 333 | /* */ |
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| 334 | /* Restore old class distribution figures of discrete attribute */ |
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| 335 | /* values x and y from Slice1 and Slice2 */ |
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| 336 | /* */ |
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| 337 | /*************************************************************************/ |
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| 338 | |
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| 339 | |
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| 340 | Uncombine(x, y) |
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| 341 | /* --------- */ |
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| 342 | DiscrValue x, y; |
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| 343 | { |
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| 344 | ClassNo c; |
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| 345 | |
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| 346 | ForEach(c, 0, MaxClass) |
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| 347 | { |
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| 348 | Freq[x][c] = Slice1[c]; |
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| 349 | Freq[y][c] = Slice2[c]; |
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| 350 | } |
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| 351 | |
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| 352 | ValFreq[x] = Slice1[MaxClass+1]; |
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| 353 | ValFreq[y] = Slice2[MaxClass+1]; |
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| 354 | } |
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| 355 | |
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| 356 | |
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| 357 | |
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| 358 | /*************************************************************************/ |
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| 359 | /* */ |
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| 360 | /* Print the values of attribute Att which are in the subset Ss */ |
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| 361 | /* */ |
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| 362 | /*************************************************************************/ |
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| 363 | |
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| 364 | |
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| 365 | PrintSubset(Att, Ss) |
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| 366 | /* ----------- */ |
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| 367 | Attribute Att; |
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| 368 | Set Ss; |
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| 369 | { |
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| 370 | DiscrValue V1; |
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| 371 | Boolean First=true; |
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| 372 | |
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| 373 | ForEach(V1, 1, MaxAttVal[Att]) |
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| 374 | { |
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| 375 | if ( In(V1, Ss) ) |
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| 376 | { |
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| 377 | if ( First ) |
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| 378 | { |
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| 379 | First = false; |
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| 380 | } |
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| 381 | else |
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| 382 | { |
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| 383 | printf(", "); |
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| 384 | } |
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| 385 | |
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| 386 | printf("%s", AttValName[Att][V1]); |
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| 387 | } |
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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 | /* */ |
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| 395 | /* Construct and return a node for a test on a subset of values */ |
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| 396 | /* */ |
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| 397 | /*************************************************************************/ |
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| 398 | |
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| 399 | |
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| 400 | SubsetTest(Node, Att) |
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| 401 | /* ----------- */ |
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| 402 | Tree Node; |
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| 403 | Attribute Att; |
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| 404 | { |
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| 405 | ItemCount CountItems(); |
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| 406 | short S, Bytes; |
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| 407 | |
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| 408 | Sprout(Node, Subsets[Att]); |
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| 409 | |
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| 410 | Node->NodeType = BrSubset; |
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| 411 | Node->Tested = Att; |
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| 412 | Node->Errors = 0; |
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| 413 | |
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| 414 | Bytes = (MaxAttVal[Att]>>3) + 1; |
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| 415 | Node->Subset = (Set *) calloc(Subsets[Att] + 1, sizeof(Set)); |
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| 416 | ForEach(S, 1, Node->Forks) |
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| 417 | { |
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| 418 | Node->Subset[S] = (Set) malloc(Bytes); |
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| 419 | CopyBits(Bytes, Subset[Att][S], Node->Subset[S]); |
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| 420 | } |
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| 421 | } |
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