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## a 4 ‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0

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1. 0 1 Vote histogram (so far) UF NNC Ptree Ex. 1 using 0-D Ptrees(sequences) a=a5 a6 a1’a2’a3’a4’=(000000) Identifying all training tuples in the distance=0 ring or 0ring, centered at a (exact matches ) as1-bitsof the Ptree, P=a5^a6^a1’^a2’^a3’^a4’ (we use _ for complement) There are no training points in a’s0ring! We must look further out, i.e., a’s1ring a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

2. (a5 a6a1’a2’a3’a4’) 0 1 OR UF NNC Ptree ex-1 (cont.) a’s 1ring? a=a5 a6 a1’a2’a3’a4’ = (000000) (001000) (100000) (010000) (000001) (000100) (000010) Training pts in the 1ring centered at a are given by 1-bits in the Ptree, P, constructed as follows: a5^a6^a1’^a2’^a3’^a4’ a5^a6^a1’^a2’^a3’^a4’ a5^a6^a1’^a2’^a3’^a4’ a5^a6^a1’^a2’^a3’^a4’ a5^a6^a1’^a2’^a3’^a4’ a5^a6^a1’^a2’^a3’^a4’ a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 The C=1 vote count = root count of P^C. a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 The C=0 vote count = root count of P^C. (never need to know which tuples voted) a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 C 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 P 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

3. a’s 2-ring? a=a5 a6 a1’a2’a3’a4’ = (000000) 0 1 (101000) (100010) (100100) (110000) (100001) For each of the following Ptrees, a 1-bit corresponds to a training point in a’s 2-ring: Pa5a6a1’a2‘a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6a1‘a2’a3‘a4‘Pa5a6a1‘a2‘a3’a4‘Pa5a6a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3‘a4’ 1st line first: a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 Stop here? But the other 10 Ptrees should also be considered. The fact that the 2-ring includes so many new training points is “The curse of demensionality”. a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5

4. Enfranchising the rest of a’s 2-ring? a=a5 a6 a1’a2’a3’a4’ = (000000) 0 1 For each of the following Ptrees, a 1-bit corresponds to a training point in a’s 2-ring: Pa5a6a1’a2‘a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6a1‘a2’a3‘a4‘Pa5a6a1‘a2‘a3’a4‘Pa5a6a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3‘a4’ 2nd line: a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5

5. Enfranchising the rest of a’s 2-ring (cont.) a=a5 a6 a1’a2’a3’a4’ = (000000) 0 1 For each of the following Ptrees, a 1-bit corresponds to a training point in a’s 2-ring: Pa5a6a1’a2‘a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘ Pa5a6a1‘a2’a3‘a4‘Pa5a6a1‘a2‘a3’a4‘Pa5a6a1‘a2‘a3‘a4’ Pa5a6 a1‘a2’a3‘a4‘Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3’a4‘Pa5a6 a1‘a2‘a3‘a4’ Pa5a6 a1‘a2‘a3‘a4’ 3rd line: a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5

6. Pts in the 47-disk, each Gets at least a vote of 1/24 Pts in the 47-disk, each Gets at least a vote of 1/12 Pts in the 47-disk, each Gets at least a vote of 1/48 PNNCvote = 1/(1/d) d(p,q) = {wi : p & q differ at i; i in the relevant_attribute_set} One way to address the curse of dimensionality is to require that all relevant attribute weights be different (except for small groups (3?) of equally weighted attributes, and that the next weight always be larger than the previous weight-sum. a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 Weights: 2 12 2 6 24 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 Vote Weight .02 .02 .02 .02 .02 .02 .02 .02 .02 .02 Vote Weight .02 .06 .06 .06 .06 .02 .02 .02 .06 .02 Vote Weight .02 .12 .12 .12 .06 .02 .02 .02 .12 .02 0-ring at 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1

7. PNNCusing weights (about the only way to address the curse of dimensionality) “Gaussian” type of vote weighting = 1/e-dis2 d(p,q) = {weighti : p & q differ at i} a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 5 2 2 9 4 4 9 9 2 1 6 6 9 9 9 9 9 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

8. a’s 1ring? a=a5 a6 a1’a2’a3’a4’ = (010010) (110010) (000010) attribute weights (1, 1, 3, 3, 3, 3) vote weight = 1/(1+distance) d(p,q) = {weighti : p & q differ at i} a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

9. a’s 2ring? a=a5 a6 a1’a2’a3’a4’ = (010010) (100010) Distance fctn: d(p,q) = {weighti : p & q differ at i} vote function: vote = 1/(1+distance) a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

10. Appendix: scratch slides a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a4 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a8 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a9 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a5‘ 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 a6‘ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 a7‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a8‘ 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 a9‘ 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 d1 d2 t1 t2 t1 t3 t1 t5 t1 t6 t2 t1 t2 t7 t3 t1 t3 t2 t3 t3 t3 t5 t5 t1 t5 t3 t5 t5 t5 t7 t6 t1 t7 t2 t7 t5 C' 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 a2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a3 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1

11. Appendix: scratch slides a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a4‘ 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a3‘ 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a2‘ 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a1‘ 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0

12. Appendix: scratch slides a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a4‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a3‘ 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a2‘ 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a1‘ 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a6 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1

13. Appendix: Comprehensive Attribute types example R( a0, a1, a2, a3, a4, a5, B6,B7, C8,C9,C) Class Label Bit-maps for categorical values from, possibly several, flat categorical attributes. Numeric attributes: domains {0..7},{0..3} Hierarchical categorical (e.g., leaf_weights; inode_weights=sums) C8 C9 dairy sundries / | \ / | \ milk egg butter crafts knits toys / \ needles pins 3 5 1 2 1 1 1 2 1 1 Assume bfr=3, so RID = (3quotient,3remainder) a0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a4 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 a4 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 a2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 B61 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B62 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B63 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 B71 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 B72 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 C81 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 C82 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 C91 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 B61 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B62 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B63 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 B71 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 B72 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 C81 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 C82 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 C91 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 C93 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 C83 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C921 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C922 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C93 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 C83 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C921 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C922 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 RRN 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16

14. RRN a0 a1 a2 a3a4 a5 B6B7C8C9C 00 1 0 1 0 0 0 6 1 {m, b}{c }1 01 1 0 1 0 0 0 6 1 { b}{ t}1 02 1 0 1 0 0 0 6 1 { e }{ n,p }1 03 1 0 1 0 0 0 6 2 {m, b}{ t}1 04 0 1 1 0 1 1 0 2 {m }{ n,p }1 05 0 1 1 0 1 1 0 0 {m,e }{ n,p }1 06 0 1 0 0 1 0 1 2 {m }{ n,p }1 07 0 1 0 0 1 0 1 1 {m, b}{c }1 08 0 1 0 0 1 0 1 1 { b}{ t}1 09 0 1 0 0 1 0 1 1 { e }{ n,p }1 10 0 1 0 1 0 0 6 2 {m }{ n,p }0 11 0 1 0 1 0 0 6 1 { b}{ t}0 12 0 1 0 1 0 0 6 1 { e }{ n,p }0 13 0 1 0 1 0 0 6 0 {m,e }{ n,p }0 14 1 0 1 0 1 0 1 2 {m }{ n,p }0 15 0 0 1 1 0 0 6 1 {m, b}{c }0 16 0 0 1 1 0 0 6 1 { e }{ n,p }0 Distance fctn: d(p,q)={wi : p & q differ at i} must have: w61=2*w62=4*w63w71=2*w72 w93=2*w921=2*w922=2*w91w83=w82=w81 Vote function: vote= 1/(1+distance) wi : 1 0 0 2 9 0 8 4 26 33 3 3 2 2 2 4 a0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a4 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 a4 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 a2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 B61 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B62 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B63 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 B71 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 B72 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 C81 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 C82 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 C91 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 B61 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B62 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B63 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 B71 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 B72 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 C81 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 C82 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 C91 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 C93 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 C83 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C921 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C922 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C93 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 C83 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C921 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C922 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 RRN 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16

15. C93 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 C922 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C921 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 unclassified sample 0-ring: C91 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 C83 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C82 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 C81 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 B72 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 B71 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 B63 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 Distance fctn: d(p,q)={wi : p & q differ at i} must have: w61=2*w62=4*w63w71=2*w72 w93=2*w921=2*w922=2*w91w83=w82=w81 Vote function: vote= 1/(1+distance) B62 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B61 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a4 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 3 9 0 8 4 2 6 3 3 3 3 2 2 2 4 wi a3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 a3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 a4 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 a5 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 a4 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 a5 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 a1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 a2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 C 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 a0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 a1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 a2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 B61 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B62 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 B63 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 B71 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 B72 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 C81 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 C82 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 C91 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 B61 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B62 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 B63 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 B71 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 B72 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 C81 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 C82 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 C91 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 C93 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 C83 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C921 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C922 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C93 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 C83 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 C921 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 C922 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0