Decision Tree for Play Tennis Outlook Sunny Rain

Decision Tree for Play. Tennis Outlook Sunny Rain Overcast Humidity High No Wind Yes Normal Yes Strong No Weak Yes

Training Examples Day Outlook 天候 Temperature 温度 Humidity 湿度 Wind 風 Play Tennis D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 D 12 D 13 D 14 Sunny Overcast Rain Overcast Sunny Rain Sunny Overcast Rain Hot Hot Mild Cool Mild Hot Mild High Normal Normal High Weak Strong Weak Weak Strong Weak Strong No No Yes Yes Yes No

Top-down Induction of Decision Tree Main loop: 1. A ← the best decision attribute for next node 2. Assign A as decision attribute for node 3. For each value of A, create new descendant of node 4. Sort training examples to leaf nodes 5. If training examples perfectly classified, then HALT, else iterate over new leaf nodes.

Which attribute is the best? [29+, 35 -] T [21+, 5 -] A 1=? F [8+, 30 -] [29+, 35 -] T [18+, 33 -] A 2=? F [11+, 2 -]

Entropy • • S is a sample of training examples p+ is the proportion of positive examples in S p- is the proportion of negative examples in S Entropy measures the impurity of S

Entropy（エントロピー） Entropy Proportion p+

Which attribute is the best? [29+, 35 -] T [21+, 5 -] A 1=? F [8+, 30 -] [29+, 35 -] T [18+, 33 -] A 2=? F [11+, 2 -]

Which is the best? - Selecting the next attribute - high [3+, 4 -], E=0. 985 S[9+, 5 -], E=0. 940 Humidity Wind normal [6+, 1 -], E=0. 592 Gain(S, Humidity)=0. 151 weak [6+, 2 -], E=0. 811 Gain(S, Wind)=0. 048 strong [3+, 3 -], E=1. 00

Training Examples Day Outlook 天候 Temperature 温度 Humidity 湿度 Wind 風 Play Tennis D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 D 12 D 13 D 14 Sunny Overcast Rain Overcast Sunny Rain Sunny Overcast Rain Hot Hot Mild Cool Mild Hot Mild High Normal Normal High Weak Strong Weak Weak Strong Weak Strong No No Yes Yes Yes No

Outlookに着目する場合 • Sunny • Overcast • Rain [2+, 3 -] [4+, 0 -] [3+, 2 -]

Temperatureに着目する場合 • Hot • Mild • Cool [2+, 2 -] [4+, 2 -] [3+, 1 -]

Humidityに着目する場合 • High • Normal [3+, 4 -] [6+, 1 -]

Decision Tree for Play. Tennis Outlook Sunny Rain Overcast Humidity High No Wind Yes Normal Yes Strong No Weak Yes