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Machine Learning Techniques · Quiz 1 · 26 Oct 2025 · September 2025 term

Question 3: Consider the dataset consisting of the following points: …

Question 3

+4 marksOne or more correct options

Consider the dataset consisting of the following points:

(0,0),  (0,2),  (2,0),  (2,2).(0, 0), \; (0, 2), \; (2, 0), \; (2, 2).

We want to run the KK-means++ algorithm with K=2K = 2. Suppose the first cluster center chosen is (0,0)(0, 0). Which of the following statements are correct?

Hint: The score of a datapoint xx is given by S(x)=min⁡j=1,2,…,l−1(∣∣x−μj0∣∣2)S(x) = \min_{j=1,2,\ldots,l-1} (||x - \mu_j^0||^2), where μj0\mu_j^0 is the initial cluster center.

Select all that apply.

  1. A

    The points (0, 2), (2, 0), and (2, 2) have the equal probability of being chosen as the second cluster center.

  2. B

    The probability of selecting (2, 2) as the second cluster center is twice that of selecting (0, 2).

  3. C

    If (2, 2) is chosen as the second cluster center, the algorithm will always converge in one iteration.

  4. D

    The tie-breaking rule will affect the final cluster centers.

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Correct answers

  • B

    The probability of selecting (2, 2) as the second cluster center is twice that of selecting (0, 2).

  • C

    If (2, 2) is chosen as the second cluster center, the algorithm will always converge in one iteration.

  • D

    The tie-breaking rule will affect the final cluster centers.

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Question 3 of 14 in the IIT Madras BS Machine Learning Techniques (MLT) Quiz 1 paper sat on 26 Oct 2025, in the September 2025 term (IIT M DIPLOMA AN EXAM QDD2 26 Oct 2025). It carries 4 marks.

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