GATE 2024 DA – Question 53
Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares.
[Figure: four small scatter plots on a 3 by 3 grid. (i) has circles at (1,3), (2,3), (1,2) and squares at (2,1), (3,1), (2,0.5). (ii) has squares at (2,3), (1,2), (3,2), (2,1) and a circle at the centre (2,2). (iii) has squares at (1,3) and (3,1) and circles at (3,3) and (1,1). (iv) has squares at about (1,2.2), (1,1.2) and (2.2,2.6) and circles at about (2,0.4), (3,1.5) and (3,0.6).]
Which of the following is/are TRUE?
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Correct answer: (A) (i) is linearly separable.; (D) (iv) is linearly separable.
Explanation
(i): the circles lie in the upper left and the squares in the lower right, so a diagonal line such as $y = x + 0.5$ separates them. (ii): the circle is in the middle of the four squares, so no line separates it from all of them. (iii): this is the XOR pattern, with the same class on the diagonal corners, which no line separates. (iv): the squares are on the upper left and the circles on the lower right, and a line such as $y = 1.3x - 0.5$ has all the squares above it and all the circles below it. So (i) and (iv) are separable.