GATE DA 2024 Set 1 — Question 53
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Question
Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares.
Which of the following is/are TRUE?
Which of the following is/are TRUE?
Correct answer
(A) (i) is linearly separable.; (D) (iv) is linearly separable.
Solution
We analyze the linear separability of each dataset:(i) The circles are at approximately (1,1), (2,2), (1,3) and squares at (2,1), (3,1). A line such as can separate them. For circles: , , (all satisfy ). For squares: , (all satisfy ). Thus, (i) is linearly separable.(ii) The squares surround a central circle. This is a classic non-linearly separable configuration (requires a radial basis function or similar).(iii) This resembles the XOR problem. Points (1,3) and (2,1) are squares, while (1,1) and (2,3) are circles. No single straight line can separate these classes.(iv) The squares are at (specifically (1,2), (2,1), (2,3)) and circles are at (specifically (3,2), (3,1)). A vertical line perfectly separates the squares (left) from the circles (right). Thus, (iv) is linearly separable.Correct options are (A) and (D).
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