Decision Tree Problem, Part 1

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Reference: P. Winston, 1992.

Factors Affecting Sunburn

Given Data

Independent Attributes / Condition Attributes

Dependent Attributes / Decision Attributes

Name	Hair	Height	Weight	Lotion	Result
Sarah	blonde	average	light	no	sunburned (positive)
Dana	blonde	tall	average	yes	none (negative)
Alex	brown	short	average	yes	none
Annie	blonde	short	average	no	sunburned
Emily	red	average	heavy	no	sunburned
Pete	brown	tall	heavy	no	none
John	brown	average	heavy	no	none
Katie	blonde	short	light	yes	none

Phase 1: From Data to Tree

1. Perform average entropy calculations on the complete data set for each of the four attributes:

b1 = blonde b2 = red b3 = brown

Average Entropy = 0.50

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b1 = short b2 = average b3 = tall

Average Entropy = 0.69

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b1 = light b2 = average b3 = heavy

Average Entropy = 0.94

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b1 = no b2 = yes

Average Entropy = 0.61

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Results

Attribute	Average Entropy
Hair Color	0.50
Height	0.69
Weight	0.94
Lotion	0.61

The attribute "hair color" is selected as the first test because it minimizes the entropy.

2. Similarily, we now choose another test to separate out the sunburned individuals from the blonde haired inhomogeneous subset, {Sarah, Dana, Annie, and Katie}.

Results

Attribute	Average Entropy
Height	0.50
Weight	1.00
Lotion	0.00

The attribute "lotion" is selected because it minimizes the entropy in the blonde hair subset.

Thus, using the "hair color" and "lotion" tests together ensures the proper identification of all the samples.

This is the completed decision tree.

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