Page 84 - Data Science Algorithms in a Week

Decision Trees

4. Mary and temperature preferences. Let us take the example from the Chapter 1,
Classification Using K Nearest Neighbors, about the temperature preferences of
Mary.

Temperature in degrees Celsius Wind speed in kmph Mary's perception
10 0 Cold
25 0 Warm
15 5 Cold
20 3 Warm
18 7 Cold
20 10 Cold
22 5 Warm
24 6 Warm
We would like to use decision trees to decide if our friend Mary would feel warm or cold in
the room with the temperature 16 degrees Celsius with the fan of the wind speed 3km/h.

Can you please explain how a decision tree algorithm could be used here and how good it
would be to use it for this example?

Analysis:

1. Here are entropies of the multisets:

a) E({1,2})=-(1/2)*log (1/2)-(1/2)*log (1/2)=1
2
2
b) E({1,2,3})=-(1/3)*log (1/3)-(1/3)*log (1/3)-(1/3)*log (1/3)=1.5849625
2
2
2
c) E({1,2,3,4})=-(1/4)*log (1/4)-(1/4)*log (1/4)-(1/4)*log (1/4)-(1/4)*log (1/4)=2
2
2
2
2
d) E({1,1,2,2})=-(2/4)*log (2/4)-(2/4)*log (2/4)=1
2
2
e) E({1,1,2,3})=-(2/4)*log (2/4)-(1/4)*log (1/4)-(1/4)*log (1/4)=1.5
2
2
2

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