Problem 1
You are a robot in a lumber yard, and must learn to discriminate Oak wood from Pine wood. You choose to learn a Decision Tree classifier. You are given the following examples:
Example
Density
Grain
Hardness
Class
Example #1
Heavy
Small
Hard
Oak
Example #2
Heavy
Large
Hard
Oak
Example #3
Heavy
Small
Hard
Oak
Example #4
Light
Large
Soft
Oak
Example #5
Light
Large
Hard
Pine
Example #6
Heavy
Small
Soft
Pine
Example #7
Heavy
Large
Soft
Pine
Example #8
Heavy
Small
Soft
Pine
1.1 Which attribute will be chosen as the root of the tree (show derivations)?
1.2 Derive the complete decision tree by recursively applying the smallest entropy criterion to select root nodes of sub-trees (show derivations). Then draw the complete decision tree.
Problem 2
NASA wants to discriminate Martians (M) from Humans (H) based on these features (attributes): Green ∈ {N, Y}, Legs∈ {2,3}, Height∈ {S, T}, Smelly ∈ {N, Y}. Your available training data is as follows (N=No, Y=Yes, S=Short, T=Tall):
(h) Derive the complete decision tree by recursively applying the smallest entropy criterion to select root nodes of sub-trees (show derivations). Then draw the complete decision tree.
