a 4 ‘ 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0
DESCRIPTION
0 1. Vote histogram (so far). UF NNC Ptree Ex. 1 using 0-D Ptrees (sequences) a=a 5 a 6 a 1 ’a 2 ’a 3 ’a 4 ’=(000000). - PowerPoint PPT PresentationTRANSCRIPT
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
UF NNC Ptree Ex. 1 using 0-D Ptrees (sequences) a=a5 a6
a1’a2’a3’a4’=(000000)
C'11001011101100110
d1 d2
t1 t2t1 t3t1 t5t1 t6t2 t1t2 t7t3 t1t3 t2t3 t3t3 t5t5 t1t5 t3t5 t5t5 t7t6 t1 t7 t2t7 t5
a1
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
0000111111000 0100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
a6
11110011111111111
a5
11110000001111011
Identifying all training tuples in the distance=0 ring or 0ring, centered at a (exact matches ) as 1-bits of the Ptree, P=
a5^a6^a1’^a2’^a3’^a4’ (we use _ for complement)
There are no training points in a’s 0ring!We must look further out, i.e., a’s 1ring
P00000000000000000
0 1Vote histogram
(so far)
C
11111111110000000
C
00000000001111111
UF NNC Ptree ex-1 (cont.) a’s 1ring? a=a5 a6 a1’a2’a3’a4’ = (000000)
C'11001011101100110
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
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
00001111110000100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
Training pts in the 1ring centered at a are given by 1-bits in the Ptree, P, constructed as follows:
0 1P01000000000100000
The C=1 vote count = root count of P^C.The C=0 vote count = root count of P^C.(never need to know which tuples voted)
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
00001111110000100
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
0 0001100000000000
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
00011010001000100
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
1 1100001110110011
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
1 0011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
0 0100100010011001
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
OR
a5^a6^a1’^a2’^a3’^a4’a5^a6^a1’^a2’^a3’^a4’
(100000)
a5^a6^a1’^a2’^a3’^a4’
(010000)
a5^a6^a1’^a2’^a3’^a4’
(001000)
a5^a6^a1’^a2’^a3’^a4’
(000100)
a5^a6^a1’^a2’^a3’^a4’
(000010)(000001)
(a5 a6 a1’a2’a3’a4’)
a’s 2-ring? a=a5 a6 a1’a2’a3’a4’ = (000000)
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
a5
0000111111000 0100
a6
00001100000000000
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
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‘ 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’Pa5a6 a1‘a2‘a3’a4‘ Pa5a6 a1‘a2‘a3‘a4’Pa5a6 a1‘a2‘a3‘a4’ 1st line first:
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
0 0001100000000000
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
00011010001000100
a6
11110011111111111
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
1 1100001110110011
a1‘
11100101110111011
a6
11110011111111111
a4‘
11011011101100110
a3‘
1 0011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a4‘
0 0100100010011001
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
00001111110000100
a5
00001111110000100
a5
00001111110000100
a5
00001111110000100
a5
00001111110000100
0 1
(110000)(101000)(100100)(100010)(100001)
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”.
Enfranchising the rest of a’s 2-ring? a=a5 a6 a1’a2’a3’a4’ = (000000)
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
a5
0000111111000 0100
a6
00001100000000000
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
0 1
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
00011010001000100
a6
0 0001100000000000
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
11100001110110011
a1‘
11100101110111011
a6
0 0001100000000000
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
11100001110110011
a2‘
00011110001001100
a1‘
11100101110111011
a6
0 0001100000000000
a5
1111000000111 1011
a4‘
00100100010011001
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
0 0001100000000000
a5
1111000000111 1011
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‘ 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’Pa5a6 a1‘a2‘a3’a4‘ Pa5a6 a1‘a2‘a3‘a4’Pa5a6 a1‘a2‘a3‘a4’ 2nd line:
Enfranchising the rest of a’s 2-ring (cont.) a=a5 a6 a1’a2’a3’a4’ = (000000)
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
a5
0000111111000 0100
a6
00001100000000000
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
0 1
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
11100001110110011
a1‘
00011010001000100
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
10011111001001110
a2‘
00011110001001100
a1‘
00011010001000100
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
00011010001000100
a6
11110011111111111
a5
1111000000111 1011
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‘ 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’Pa5a6 a1‘a2‘a3’a4‘ Pa5a6 a1‘a2‘a3‘a4’Pa5a6 a1‘a2‘a3‘a4’ 3rd line:
PNNC vote = 1/(1/d)
C'11001011101100110
d1 d2
t1 t2t1 t3t1 t5t1 t6t2 t1t2 t7t3 t1t3 t2t3 t3t3 t5t5 t1t5 t3t5 t5t5 t7t6 t1 t7 t2t7 t5
a1
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
0000111111000 0100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
d(p,q) = {wi : p & q differ at i; i in the relevant_attribute_set}
0-ring at 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1
Weights:
0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1
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.
12 2 612 24a7‘ 00101110011011101
Pts in the 47-disk, eachGets at least a vote of 1/48
Vote Weight
.02 .02.02.02 .02.02 .02.02.02 .02
a5
0000111111000 0100
Vote Weight
.02 .06.06.06 .06.02 .02.02.06 .02
Pts in the 47-disk, eachGets at least a vote of 1/24
a3‘
10011111001001110
Pts in the 47-disk, eachGets at least a vote of 1/12
Vote Weight
.02 .12.12.12 .06.02 .02.02.12 .02
a4‘
11011011101100110
a3‘
10011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
PNNC using weights (about the only way to address the curse of dimensionality)“Gaussian” type of vote weighting = 1/e-dis2
C'11001011101100110
d1 d2
t1 t2t1 t3t1 t5t1 t6t2 t1t2 t7t3 t1t3 t2t3 t3t3 t5t5 t1t5 t3t5 t5t5 t7t6 t1 t7 t2t7 t5
a1
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
0000111111000 0100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
a6
00001100000000000
a5
11110000001111011
d(p,q) = {weighti : p & q differ at i}
P00000000000000000
1 5 2 2 9 4 4 9 9 2 1 6 6 9 9 9 9 9
a’s 1ring? a=a5 a6 a1’a2’a3’a4’ = (010010)
C'11001011101100110
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
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
00001111110000100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
P00000000000000000
a4‘
11011011101100110
a3‘
10011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
a6
00001100000000000
a5
00001111110000100
a4‘
11011011101100110
a3‘
10011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
attribute weights (1, 1, 3, 3, 3, 3) vote weight = 1/(1+distance) d(p,q) = {weighti : p & q differ at i}
(110010)(000010)
a’s 2ring? a=a5 a6 a1’a2’a3’a4’ = (010010)
C'11001011101100110
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
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
00001111110000100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
P00000000000000000
a4‘
11011011101100110
a3‘
10011111001001110
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
00001111110000100
Distance fctn: d(p,q) = {weighti : p & q differ at i} vote function: vote = 1/(1+distance)
(100010)
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
C'11001011101100110
d1 d2
t1 t2t1 t3t1 t5t1 t6t2 t1t2 t7t3 t1t3 t2t3 t3t3 t5t5 t1t5 t3t5 t5t5 t7t6 t1 t7 t2t7 t5
a1
11110000000000100
a2 00001111111111000
a3
11111100000000111
a4
000000000 01111011
a5
0000111111000 0100
a6
00001100000000000
a7
11110000001111011
a8
11110000001111011
a9
00000011110000100
C11111111110000000
a1‘00011010001000100
a2‘ 11100001110110011
a3‘ 10011111001001110
a4‘ 00100100010011001
a5‘ 110100011001000 10
a6‘10000001000000010
a7‘ 00101110011011101
a8‘00101110011011101
a9‘01010000100100000
a6
00001100000000000
a5
0000111111000 0100
Appendix: scratch slides
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
Appendix: scratch slides
a4‘
00100100010011001
a3‘
10011111001001110
a2‘
11100001110110011
a1‘
00011010001000100
a6
00001100000000000
a5
0000111111000 0100
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
Appendix: scratch slides
a4‘
11011011101100110
a3‘
01100000110110001
a2‘
00011110001001100
a1‘
11100101110111011
a6
11110011111111111
a5
1111000000111 1011
RRN
000102030405060708091011121314 1516
a0
11110000000000100
a1 00001111111111000
a2
11111100000000111
a3
000000000 01111011
a4
0000111111000 0100
a5
00001100000000000
B61
11110000001111011
B62
11110000001111011
B63
00000011110000100
C11111111110000000
B71
00011010001000100
B72
11100001110110011
C81 10011111001001110
C82 00100100010011001
C83 110100011001000 10
C91
10000001000000010
C921 00101110011011101
C922
00101110011011101
C93
01010000100100000
Appendix: Comprehensive Attribute types exampleR( a0, a1, a2, a3, a4, a5, B6,B7, C8,C9,C)
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 1
1 1 1 2
1
2
53
Assume bfr=3, so RID = (3quotient,3remainder)
1
Class Label
a0
00001111111111011
a1 11110000000000111
a2
00000011111111000
a3
11111111110000100
a4
11110000001111011
a5
11110011111111111
B61
00001111110000100
B62
00001111110000100
B63
11111100001111011
B71
11100101110111011
B72
00011110001001100
C81 01100000111110001
C82 11011011101100110
C83 001011100110111 01
C91
01111110111111101
C921 11010001100100010
C922
11010001100100010
C93
10101111011011111
RRN a0 a1 a2 a3 a4 a5 B6 B7 C8 C9 C00 1 0 1 0 0 0 6 1 {m, b} {c } 101 1 0 1 0 0 0 6 1 { b} { t} 102 1 0 1 0 0 0 6 1 { e } { n,p } 103 1 0 1 0 0 0 6 2 {m, b} { t} 104 0 1 1 0 1 1 0 2 {m } { n,p } 105 0 1 1 0 1 1 0 0 {m,e } { n,p } 106 0 1 0 0 1 0 1 2 {m } { n,p } 107 0 1 0 0 1 0 1 1 {m, b} {c } 108 0 1 0 0 1 0 1 1 { b} { t} 109 0 1 0 0 1 0 1 1 { e } { n,p } 110 0 1 0 1 0 0 6 2 {m } { n,p } 011 0 1 0 1 0 0 6 1 { b} { t} 012 0 1 0 1 0 0 6 1 { e } { n,p } 013 0 1 0 1 0 0 6 0 {m,e } { n,p } 014 1 0 1 0 1 0 1 2 {m } { n,p } 015 0 0 1 1 0 0 6 1 {m, b} {c } 016 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*w63
w71=2*w72
w93=2*w921=2*w922=2*w91 w83=
w82=w81
Vote function: vote= 1/(1+distance)
RRN
0001020304050607080910111213141516
a0
11110000000000100
a1 00001111111111000
a2
11111100000000111
a3
000000000 01111011
a4
0000111111000 0100
a5
00001100000000000
B61
11110000001111011
B62
11110000001111011
B63
00000011110000100
C11111111110000000
B71
00011010001000100
B72
11100001110110011
C81 10011111001001110
C82 00100100010011001
C83 11010001100100010
C91
10000001000000010
C921 00101110011011101
C922
00101110011011101
C93
01010000100100000
a0
00001111111111011
a1 11110000000000111
a2
00000011111111000
a3
11111111110000100
a4
11110000001111011
a5
11110011111111111
B61
00001111110000100
B62
00001111110000100
B63
11111100001111011
B71
11100101110111011
B72
00011110001001100
C81 01100000111110001
C82 11011011101100110
C83 001011100110111 01
C91
01111110111111101
C921 11010001100100010
C922
11010001100100010
C93
10101111011011111
wi : 1 0 0 2 9 0 8 4 2 6 3 3 3 3 2 2 2 4
Distance fctn: d(p,q)={wi : p & q differ at i} must have: w61=2*w62=4*w63
w71=2*w72
w93=2*w921=2*w922=2*w91 w83=
w82=w81
Vote function: vote= 1/(1+distance)
a0
11110000000000100
a1 00001111111111000
a2
11111100000000111
a3
000000000 01111011
a4
0000111111000 0100
a5
00001100000000000
B61
11110000001111011
B62
11110000001111011
B63
00000011110000100
C11111111110000000
B71
00011010001000100
B72
11100001110110011
C81 10011111001001110
C82 00100100010011001
C83 11010001100100010
C91
10000001000000010
C921 00101110011011101
C922
00101110011011101
C93
01010000100100000
a0
00001111111111011
a1 11110000000000111
a2
00000011111111000
a3
11111111110000100
a4
11110000001111011
a5
11110011111111111
B61
00001111110000100
B62
00001111110000100
B63
11111100001111011
B71
11100101110111011
B72
00011110001001100
C81 01100000111110001
C82 11011011101100110
C83 001011100110111 01
C91
01111110111111101
C921 11010001100100010
C922
11010001100100010
C93
10101111011011111
0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 unclassified sample 0-ring:
1 0 0 3 9 0 8 4 2 6 3 3 3 3 2 2 2 4 wi a0
00001111111111011
a3
000000000 01111011
a4
11110000001111011
B61
11110000001111011
B62
11110000001111011
B63
00000011110000100
B71
11100101110111011
B72
11100001110110011
C81
01100000111110001
C82
11011011101100110
C83
11010001100100010
C91
01111110111111101
C921
00101110011011101
C922
00101110011011101
C93
10101111011011111