Decision Tree Prof. Seungchul Lee Industrial AI Lab.
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Feature test in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 2
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 3 Feature 2 Yes No Good: 0 Good: 3 Bad: 3 Bad: 2 3
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 3 2 Feature 2 Feature 3 Medium Low High Yes No Good: 0 Good: 3 Good: 2 Good: 0 Good: 1 Bad: 3 Bad: 2 Bad: 1 Bad: 2 Bad: 2 4
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 3 2 0 Feature 2 Feature 3 Feature 4 Medium Low High Medium Low High Yes No Good: 0 Good: 3 Good: 2 Good: 0 Good: 1 Good: 1 Good: 1 Good: 1 Bad: 3 Bad: 2 Bad: 1 Bad: 2 Bad: 2 Bad: 2 Bad: 1 Bad: 2 5
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 6
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 7
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 4 Feature 2 Yes No Good: 0 Good: 2 Bad: 2 Bad: 0 8
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 4 2 Feature 2 Feature 3 Medium Low High Yes No Good: 0 Good: 2 Good: 1 Good: 0 Good: 1 Bad: 2 Bad: 0 Bad: 0 Bad: 1 Bad: 1 9
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 4 2 0 Feature 2 Feature 3 Feature 4 Medium Low High Medium Low High Yes No Good: 0 Good: 2 Good: 1 Good: 0 Good: 1 Good: 1 Good: 1 Good: 0 Bad: 2 Bad: 0 Bad: 0 Bad: 1 Bad: 1 Bad: 1 Bad: 1 Bad: 0 10
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Homogeneous set in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good 4 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 4 Feature 2 Yes No Good: 0 Good: 2 Bad: 2 Bad: 0 11
Feature Test Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Decision tree Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 0 Good: 1 Feature 2 Bad: 3 Bad: 0 Yes No Good: 0 Good: 2 Bad: 2 Bad: 0 • Issue: a large data set will be most likely to produce zero homogeneous set 12
Disorder • Disorder of single set 13
Quality of Test • Disorder of single set • Quality of test Q = 0.5 Feature 1 4 3 1 8 ? Yes 8 No 8 Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 14
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad 4 3 1 Yes No Medium High Bad 8 ? Yes 8 No 8 ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 Q = 0.6 Feature 2 3 5 Yes No 8 8 Good: 0 Good: 3 Bad: 3 Bad: 2 D = 0 D = 0.97 15
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad 4 3 1 Yes No Medium High Bad 8 ? Yes 8 No 8 ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 Q = 0.6 Q = 0.69 Feature 2 Feature 3 3 3 2 3 5 Medium Low High Yes No 8 8 8 8 8 Good: 0 Good: 3 Good: 2 Good: 0 Good: 1 Bad: 3 Bad: 2 Bad: 1 Bad: 2 Bad: 2 D = 0 D = 0.97 D = 0.92 D = 0 D = 0.92 16
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad 4 3 1 Yes No Medium High Bad 8 ? Yes 8 No 8 ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 Q = 0.6 Q = 0.69 Q = 0.94 Feature 2 Feature 3 Feature 4 3 3 2 3 3 2 3 5 Medium Low High Medium Low High Yes No 8 8 8 8 8 8 8 8 Good: 0 Good: 3 Good: 2 Good: 0 Good: 1 Good: 1 Good: 1 Good: 1 Bad: 3 Bad: 2 Bad: 1 Bad: 2 Bad: 2 Bad: 2 Bad: 1 Bad: 2 D = 0 D = 0.97 D = 0.92 D = 0 D = 0.92 D = 0.92 D = 1 D = 0.92 17
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the first level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad 4 3 1 Yes No Medium High Bad 8 ? Yes 8 No 8 ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 18
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 19
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 Q = 0 Feature 2 2 2 Yes No 4 4 Good: 0 Good: 2 Bad: 2 Bad: 0 D = 0 D = 0 20
Quality Feature 1 Feature 2 Feature 3 Feature 4 output ? Yes Low Medium Bad • Quality of test in the second level Yes Yes High Medium Bad ? No High Medium Good No No Medium High Good ? No Medium Low Good Q = 0.5 Feature 1 Yes No Low High Bad Yes No Medium High Bad ? Yes No ? Yes High Low Bad Good: 2 Good: 0 Good: 1 Bad: 2 Bad: 3 Bad: 0 D = 1 D = 0 D = 0 Q = 0 Q = 0.5 Feature 2 Feature 3 2 2 1 1 2 Medium Low High Yes No 4 4 4 4 4 Good: 0 Good: 2 Good: 1 Good: 0 Good: 1 Bad: 2 Bad: 0 Bad: 0 Bad: 1 Bad: 1 D = 0 D = 0 D = 0 D = 0 D = 1 21
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