Question10 Which of the following statements is/are INCORRECT about the parameter C in soft margin SVM, which controls the complexity of the model: (you can choose more than one) A high value of C means that margin errors will have a high penalty If C is set to infinity ([math]) , then the optimal hyperplane (if it exists), will completely separates the classes If C is set to zero, then the optimal hyperplane will always have small training error A low value of C permits more margin errors ResetMaximum marks: 2 Flag question undefined

Question

Question10 Which of the following statements is/are INCORRECT about the parameter C in soft margin SVM, which controls the complexity of the model: (you can choose more than one) A high value of C means that margin errors will have a high penalty If C is set to infinity ([math]) , then the optimal hyperplane (if it exists), will completely separates the classes If C is set to zero, then the optimal hyperplane will always have small training error A low value of C permits more margin errors ResetMaximum marks: 2 Flag question undefined

BlackTom AI · Accepted Answer

Question: Which of the following statements is/are INCORRECT about the parameter C in soft margin SVM, which controls the complexity of the model: (you can choose more than one)

Option 1: 'A high value of C means that margin errors will have a high penalty.'
This statement is true. In soft-margin SVM, C controls the trade-off between margin width and classification error. A large C places a heavy penalty on misclassified or margin-violating points, pushing the optimizer to reduce those errors even at the cost of a smaller margin. Therefore, this option is not incorrect.

Option 2: 'If C is set to infinity (C → ∞), then the optimal hyperplane (if it exists) will completely separate the classes.'
This statement is effectively describing the hard-margin limit. As C grows very large, the optimization emphasizes removing all margin violations, which (when the data are linearly separable) yields a hard-margin solution that perfectly separates the classes. However, note that if the data are not linearly separable, no such hyperplane exists. The essence of the claim is correct in the separable case, so this option is not incorrect in the standard interpretation.

Option 3: 'If C is set to zero, then the optimal hyperplane will always have small training error.'
This statement is incorrect. When C → 0, the optimization prioritizes margin maximization with almost no penalty for misclassifications. The model tends to favor a wider margin even if it increases training error, so it does not guarantee small training error. In fact, training error can be large because the objective de-emphasizes misclassified points. Thus, this option is indeed incorrect.

Option 4: 'A low value of C permits more margin errors.'
This statement is true. A smaller C reduces the penalty for violations, allowing more slack and hence more margin errors in the training data. Therefore, this option is not incorrect.

Summary: Only Option 3 is incorrect because it states that small C leads to small training error, which contradicts the behavior of the C parameter in soft-margin SVM. The other statements align with the established understanding of how C influences margin and misclassifications.

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