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CURRENT TREE
root node
254 +
319 −
chol
low
consider all
binary splits
67 +
124 −
entropy
trig
low med, high
37 +
30 +
70 −
54 −
trig
med
18 +
36 −
low, high
49 +
88 −
trig
high
12 +
18 −
low, med
55 +
106 −
.9334
hdl
low med, high
22 +
45 +
36 −
88 −
.9337
hdl
med
23 +
42 −
low, high
44 +
82 −
.9348
hdl
high
22 +
46 −
low, med
45 +
78 −
.9335
chol
med, high
187 +
195 −
current
node
.9347
ÑNEW TREE
root node
Ð254 +
.9344
319 −
select
best split
chol
low
chol
med, high
67 +
124 −
trig
high
12 +
18 −
187 +
195 −
trig
low, med
55 +
106 −
current
node
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INITIAL RANDOM CLASS DISTRIBUTION
227
examples
form
probabilistic
descriptions
of classes
low
med
high
106 +
121 −
chol
trig
hdl
.39
.26
.35
.42
.30
.28
.24
.36
.40
346
examples
low
med
high
148 +
198 −
chol
trig
hdl
.30
.38
.32
.28
.35
.37
.40
.30
.30
reassign
examples
based on
descriptions
CLASS DISTRIBUTION AFTER 1 ITERATION
228
examples
form
probabilistic
descriptions
of classes
low
med
high
100 +
127 −
chol
trig
hdl
.42
.27
.31
.46
.30
.24
.22
.36
.42
345
examples
low
med
high
153 +
192 −
chol
trig
hdl
.28
.38
.34
.25
.35
.40
.42
.30
.28
13 more
iterations
CLASS DISTRIBUTION AFTER 14 ITERATIONS
final
distribution
of examples
final
descriptions
of classes
308
examples
low
med
high
116 +
192 −
chol
trig
hdl
.46
.36
.18
.62
.38
.00
.08
.37
.55
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3"',2)(+'(#-&L
265
examples
low
med
high
138 +
127 −
chol
trig
hdl
.18
.31
.51
.00
.28
.72
.63
.28
.09
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í ð
CURRENT TREE
Node (with counts of positive
and negative examples)
(after 14 examples)
5+
9−
e
B
1+
1−
115
365
10 7 4
Leaf node (single example)
4
1 3
67
3+
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+ −
C
e
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1
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D
0+
4−
+ + +
− −
ADD NEW EXAMPLE
1
2
2
1
2
22
low 1
med 3
high 10
14
1
6
7
14
c
5
5
4
14
1
3
10
1
6
7
5
5
4
Each column sums to the number
of examples explained by the node
1. The new example is automatically explained by the root node (A);
check category utility for adding example to each child of root to
find the best child.
class
hdl
low
0+
2−
− −
0+
2−
chol trig
low high
−
b
3
1 1
34
− −
Each node keeps a count of the
attribute−values of the examples
explained by that node, which can
be summarized by a grid:
11
14
4 4
1+
4−
hdl
1
122
A
chol
trig
f
root node
+
2. The best child is the second child (B); also consider adding new
example as singleton, merging two best children, and splitting best
child into two.
d (Example illustrated
as a grid)
1
3. The category utility of the tree would be most improved by a "split"
of the best child. Since this node has two children (C and D), this
is equivalent to"promoting" the two children nodes to be children of
the root node.
1
1
4. The best match is with the first of these two nodes, so the example
is added to node C, and this becomes the current node; check the
category utility for adding the example to each of the three children.
NEW TREE
(after 15 examples)
f
1
122
root node
A
6+
9−
216
365
10 8 4
1+
1−
34
11
14
4 4
1+
4−
+ −
1
5. Check the category utility for creating a new singleton (leaf node),
merging two best children, and splitting best child into two. The
highest category utility of these is found to be creating a new leaf
node, so the example is added there and the recursion terminates.
+ −
2
2
C
g
4+
0−
+ + + +
D
0+
4−
3
1 1
34
−
0+
2−
− −
− −
0+
2−
− −
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31
11
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L
L
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L
L
L
L
AI
AII
B
CII
CIII
L
L
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L
L
DIA
CNT
L
L
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L
L
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22
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AII
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CII
CIII
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L
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L
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L
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L
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WT
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L
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L
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L
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L
L
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L
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L
L
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L
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22
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32
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L
L
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L
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L
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22
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32
21
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L
L
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L
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L
L
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L
L
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L
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22
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32
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31
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44
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44
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L
L
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22
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33
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33
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H H H H H H H H H H H H H H H H M Y
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31
11
L
L
L
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L
L
L
L
L
L
AI
AII
B
CII
CIII
L
E SYS
L
L
L
DIA
CNT
L
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L
L
HT
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N
M/F SMOKE
22
H H H H H H H H H H H H H H H H M Y
32
21
M M M M M M M M M M M M M M M M F
31
11
L
L
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L
L
L
L
L
L
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AII
B
CII
CIII
L
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L
L
L
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CNT
L
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L
L
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22
H H H H H H H H H H H H H H H H M Y
32
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M M M M M M M M M M M M M M M M F
31
11
L
L
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L
L
L
L
L
AI
AII
B
CII
CIII
L
E SYS
L
L
L
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CNT
L
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L
L
HT
WT
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22
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32
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44
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44
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L
L
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L
L
L
L
L
L
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CIII
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L
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32
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11
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L
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L
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L
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—
22
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32
21
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11
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L
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L
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L
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L
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22
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L
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—
21
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11
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L
L
L
L
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CII
CIII
L
L
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L
L
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L
L
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L
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N
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32
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11
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L
L
L
L
L
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AII
B
CII
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L
L
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L
L
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L
L
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L
L
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WT
N
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—
22
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32
21
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31
11
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32
L
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L
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CII
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L
L
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L
L
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21
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a=25
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L
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L
L
L
L
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CII
CIII
L
L
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L
L
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L
L
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L
L
HT
WT
N
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Michigan
Approach
One or more strings from the population
form a rule set.
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Each string in the population
represents a distinct rule set.
Pitt
Approach
Many different rule sets
are evolved in a GA run.
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run GA
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run GA
save best string
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#1
save best string
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#2
#3
remove points from data set that match against best
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33
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32
32
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42
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31
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33
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43
32
32
21
42
22
31
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33
33
22
43
32
32
21
42
22
31
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33
33
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32
32
21
42
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CHOL TRIG HDL
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L
L
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L
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L
L
HT
WT
N
M/F SMOKE
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22
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32
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31
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CHOL TRIG HDL
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L
L
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22
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