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

Question 6: Consider a mean-centered dataset consisting of 150 patien…

Question 6

+3 marksNumerical answer

Consider a mean-centered dataset consisting of 150 patients from the health-care domain with 6 features. The dataset is represented as a 150×6150 \times 6 matrix XX. PCA is performed on this dataset, and it is observed that the reconstruction error (residue) vanishes completely after kk components. A domain expert provides the following insights about the columns of XX, denoted by c1,c2,…,c6c_1, c_2, \ldots, c_6:

(a) The set {c1,c2,c3}\{c_1, c_2, c_3\} is linearly independent.

(b) The following relationships hold:

  • c4=2c1−c2c_4 = 2c_1 - c_2
  • c5=c2+c3c_5 = c_2 + c_3
  • c6=4c1−3c3c_6 = 4c_1 - 3c_3

What is the value of kk?

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Correct answer: 3

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Question 6 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 3 marks.

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