GATE DA 2025 Set 1 — Question 53
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Machine Learning → Support Vector Machines → SVM Theory
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Question
Consider designing a linear binary classifier on the following training data:Class-1: , Class-2: Hard-margin support vector machine (SVM) formulation is solved to obtain and .
Which of the following options is/are correct?
Which of the following options is/are correct?
Correct answer
(B) The number of support vectors is 3; (C) The margin is √(2)
Solution
The data points are:
Class 1 ():
Class 2 (): By inspection, the decision boundary that maximizes the margin between the convex hull of Class 1 and Class 2 is the perpendicular bisector of the segment connecting to the line segment between and .
The closest points (Support Vectors) are from Class 2, and from Class 1.The separating hyperplane is .
In canonical SVM form at the margins:
For , .
For , .
For , .
So and .(A) False: , not .
(B) True: The support vectors are . Total 3.
(C) True: Margin .
(D) False: Hard-margin SVM on linearly separable data yields 100% training accuracy.
Class 1 ():
Class 2 (): By inspection, the decision boundary that maximizes the margin between the convex hull of Class 1 and Class 2 is the perpendicular bisector of the segment connecting to the line segment between and .
The closest points (Support Vectors) are from Class 2, and from Class 1.The separating hyperplane is .
In canonical SVM form at the margins:
For , .
For , .
For , .
So and .(A) False: , not .
(B) True: The support vectors are . Total 3.
(C) True: Margin .
(D) False: Hard-margin SVM on linearly separable data yields 100% training accuracy.
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