Samples for Exam 4


Task 1

  Class     A     B     C  
X 1 2 1
X 2 1 2
X 3 2 2
X 1 3 3
X 1 2 1
Y 2 1 2
Y 3 1 1
Y 2 2 2
Y 3 3 1
Y 2 1 1

We want to build a decision tree that determines whether a certain pattern is of type X or type Y. The decision tree can only use tests that are based on attributes A, B, and C. Each attribute has 3 possible values: 1, 2, 3 (we do not apply any thresholding). We have the 10 training examples, shown on the table (each row corresponds to a training example). What is the information gain of each attribute at the root? Which attribute achieves the highest information gain at the root?

Task 2

  Class     A     B     C  
X 25
 24
 31
X 22
 14
 24
X 28
 22
 25
X 24
 13
 30
X 26
 20
 24
Y 20
 31
 17
Y 18
 32
 14
Y 21
 25
 20
Y 13
 32
 15
Y 12
 27
 18

We want to build a decision tree (which thresholding) that determines whether a certain pattern is of type X or type Y. The decision tree can only use tests that are based on attributes A, B, and C. We have the 10 training examples, shown on the table (each row corresponds to a training example). Which attribute threshold combination achieves the highest information gain at the root? For each attribute try the thresholds of 15, 20 and 25.

Task 3

Consider a Classification problem with patterns that have 30 Attributes where each attribute takes a value between 0 and 127 that have to classified as one of 10 possible class labels.