1. Teori Keputusan (Decision Theory)
Kecerdasan Buatan
Teori Keputusan
(Decision Theory)

2. Decision trees
Sebuah pohon keputusan dapat didefinisikan sebagai peta proses penalaran.

3. An example of a decision tree

4. A decision tree consists of nodes, branches and leaves.
The top node is called the root node. All nodes are connected by branches.
Nodes that are at the end of branches are called terminal nodes, or leaves.

5. Example of a Decision Tree
categorical
continuous
class
Splitting Attributes
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES
Training Data
Model: Decision Tree

6. Apply Model to Test Data
Start from the root of tree.
Refund
MarSt
TaxInc
YES NO
Yes No
Married
Single, Divorced
< 80K
> 80K

7. Apply Model to Test Data
Refund
MarSt
TaxInc
YES NO
Yes No
Married
Single, Divorced
< 80K
> 80K

8. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

9. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

10. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

11. Apply Model to Test Data
Refund
Yes No NO
MarSt
Married
Assign Cheat to “No”
Single, Divorced
TaxInc NO
< 80K
> 80K NO
YES

12. Weather Data: Play or not Play?
Outlook
Temperature
Humidity
Windy
Play?
sunny
hot
high
false No
true
overcast
Yes
rain
mild
cool
normal

13. Example Tree for “Play?”
Outlook
sunny
rain
overcast
Humidity
Yes
Windy
high
normal
true
false No
Yes No
Yes

14. Entropy at a given node t:
(NOTE: p( j | t) is the relative frequency of class j at node t).

15. Examples for computing Entropy
P(C1) = 0/6 = P(C2) = 6/6 = 1
Entropy = – 0 log 0 – 1 log 1 = – 0 – 0 = 0
P(C1) = 1/ P(C2) = 5/6
Entropy = – (1/6) log2 (1/6) – (5/6) log2 (1/6) = 0.65
P(C1) = 2/ P(C2) = 4/6
Entropy = – (2/6) log2 (2/6) – (4/6) log2 (4/6) = 0.92

16. Information Gain: Parent Node, p is split into k partitions;
ni is number of records in partition i

17. Which attribute to select?
witten&eibe

18. Example: attribute “Outlook”
“Outlook” = “Sunny”:
“Outlook” = “Overcast”:
“Outlook” = “Rainy”:
Expected information for attribute:
Note: log(0) is not defined, but we evaluate 0*log(0) as zero
witten&eibe