Question

a) Consider the dataset in Table 1. Grade, Bumpiness and Speed-limit are the features and Speed
is label.

Table 1: Dataset for decision tree

SN	Grade	Bumpiness	Speed-limit	Speed
1	steep	bumpiness	yes	slow
2	steep	smooth	yes	slow
3	flat	bumpiness	no	fast
4	steep	smooth	no	fast

Answer the followings:
i) Determine the entropy of Speed.
ii) Which attribute should be selected as a root of the decision tree?
iii) Construct the decision tree for this dataset based on information gain.

b) What to you mean by clustering? Consider the following sample points, A (1, 1), B (2, -2), C (2, 3), D (3, 3). Perform k-means clustering, show the calculation of distance matrix and group assignment matrix for two epochs only. [Assume k=2]

Answer 1

The entropy of the speed is 1.

The equation of calculating the entropy is:

Let's consider the Speed fast as Positive

And speed slow as Negative

The formula of probability is Probability is : Number of favourable outcomes/Total number of Outcomes.
Therefore Probability of the fast = 2/4 = 1/2

And Probability of slow = 2/4 = 1/2

Putting these values in the above equation we get Entropy = 1