Answer:
ID3 Algorithm is used for training a decision tree from a dataset. The steps for ID3 algorithm are as follows:
(1) Calculate the entropy of the target attribute: The entropy of the target attribute can be calculated by summing the products of the probabilities of each value of the target attribute and its logarithm base 2.
(2) Calculate the information gain for each attribute: The information gain for each attribute is calculated by subtracting the entropy of the target attribute from the entropy of the attribute after the dataset is split using the attribute.
(3) Select the attribute with the highest information gain: The attribute with the highest information gain is selected as the root node of the tree.
(4) Split the dataset based on the selected attribute: The dataset is split into subsets based on the values of the selected attribute.
(5) Create a branch for each subset and repeat steps 1-4 for each branch: For each branch, steps 1-4 are repeated until all the branches are completed.
Step-by-step explanation:
For the given data, the target attribute is "Buy?" and the other attributes are "Age", "Employment", and "Student".
Entropy of the target attribute: P(Yes) = 2/5 P(No) = 3/5
Entropy = -(2/5 * log2(2/5)) - (3/5 * log2(3/5)) = 0.971
Information gain for each attribute:
Age:
P(Youth) = 2/5 P(Middle Aged) = 2/5 P(Senior) = 1/5
Entropy of Age = -(2/5 * log2(2/5)) - (2/5 * log2(2/5)) - (1/5 * log2(1/5)) = 0.971
Information gain = 0.971 - 0.971 = 0
Employment:
P(Employed) = 2/5 P(Unemployed) = 3/5
Entropy of Employment = -(2/5 * log2(2/5)) - (3/5 * log2(3/5)) = 0.971
Information gain = 0.971 - 0.971 = 0
Student: