CS 559 Quiz 7: Support Vector Machines
(SVM) Questions and Answers | 2026
Update | 100% Correct.
Basic SVM Concepts
Q1: What is the primary objective of a Support Vector Machine?
A) To minimize classification error on training data
B) To maximize the margin between classes while minimizing classification error
C) To find the most complex decision boundary possible
D) To minimize the number of support vectors
Answer: B
Rationale: SVM aims to find the optimal hyperplane that maximizes the margin (distance)
between classes while correctly classifying as many training points as possible. This is the
fundamental principle behind SVM.
Q2: What are support vectors?
A) All training data points
B) Only the misclassified points
C) Data points that lie on or within the margin boundary
D) Randomly selected points from the training set
Answer: C
Rationale: Support vectors are the training examples that are closest to the decision
,boundary and influence the position and orientation of the separating hyperplane. They lie
on the margin boundaries or are within the margin.
Q3: In a linearly separable dataset, how many support vectors are typically
needed?
A) At least 2
B) At least 3
C) All data points
D) None
Answer: A
Rationale: In the simplest case of 2D linearly separable data, the minimum number of
support vectors required to define the margin is 2 (one from each class), though in practice
there are often more.
Q4: What is the margin in SVM?
A) The distance between the hyperplane and all data points
B) The distance between the hyperplane and the nearest data point from either class
C) The distance between the two class centers
D) The total number of misclassified points
Answer: B
Rationale: The margin is defined as the perpendicular distance from the separating
hyperplane to the nearest training data point of either class. SVM maximizes this margin.
,Q5: What is the decision function of a linear SVM?
A) f(x) = w·x + b
B) f(x) = w·x - b
C) f(x) = w² + b
D) f(x) = |w·x| + b
Answer: A
Rationale: The linear SVM decision function is f(x) = w·x + b, where w is the weight vector
and b is the bias term. The sign of f(x) determines the class prediction.
Q6: What is the hinge loss function?
A) L(y, f(x)) = max(0, 1 - y·f(x))
B) L(y, f(x)) = (y - f(x))²
C) L(y, f(x)) = |y - f(x)|
D) L(y, f(x)) = -log(1 + exp(-y·f(x)))
Answer: A
Rationale: Hinge loss is defined as max(0, 1 - y·f(x)), where y ∈ {-1, +1}. It penalizes
predictions that are on the wrong side of the margin, with no penalty for correct
predictions beyond the margin.
Q7: What does the parameter C control in SVM?
A) The learning rate
B) The trade-off between margin maximization and misclassification penalty
C) The number of support vectors
D) The kernel type
, Answer: B
Rationale: C is the regularization parameter that controls the trade-off between having a
wider margin and minimizing training error. Smaller C allows more misclassifications
(wider margin), larger C forces fewer misclassifications (narrower margin).
Q8: What happens when C approaches infinity in SVM?
A) The model becomes fully regularized
B) The model becomes a hard-margin SVM
C) The model ignores all training data
D) The model becomes a soft-margin SVM with maximum margin
Answer: B
Rationale: As C → ∞, the penalty for misclassification becomes infinitely large, forcing the
model to correctly classify all training points, effectively becoming a hard-margin SVM.
Q9: What happens when C approaches 0 in SVM?
A) The model becomes a hard-margin SVM
B) The model prioritizes margin maximization over classification accuracy
C) The model overfits the training data
D) The model becomes identical to logistic regression
Answer: B
Rationale: Small C values prioritize maximizing the margin even at the cost of
misclassifying some training points, leading to a simpler, more regularized model.
(SVM) Questions and Answers | 2026
Update | 100% Correct.
Basic SVM Concepts
Q1: What is the primary objective of a Support Vector Machine?
A) To minimize classification error on training data
B) To maximize the margin between classes while minimizing classification error
C) To find the most complex decision boundary possible
D) To minimize the number of support vectors
Answer: B
Rationale: SVM aims to find the optimal hyperplane that maximizes the margin (distance)
between classes while correctly classifying as many training points as possible. This is the
fundamental principle behind SVM.
Q2: What are support vectors?
A) All training data points
B) Only the misclassified points
C) Data points that lie on or within the margin boundary
D) Randomly selected points from the training set
Answer: C
Rationale: Support vectors are the training examples that are closest to the decision
,boundary and influence the position and orientation of the separating hyperplane. They lie
on the margin boundaries or are within the margin.
Q3: In a linearly separable dataset, how many support vectors are typically
needed?
A) At least 2
B) At least 3
C) All data points
D) None
Answer: A
Rationale: In the simplest case of 2D linearly separable data, the minimum number of
support vectors required to define the margin is 2 (one from each class), though in practice
there are often more.
Q4: What is the margin in SVM?
A) The distance between the hyperplane and all data points
B) The distance between the hyperplane and the nearest data point from either class
C) The distance between the two class centers
D) The total number of misclassified points
Answer: B
Rationale: The margin is defined as the perpendicular distance from the separating
hyperplane to the nearest training data point of either class. SVM maximizes this margin.
,Q5: What is the decision function of a linear SVM?
A) f(x) = w·x + b
B) f(x) = w·x - b
C) f(x) = w² + b
D) f(x) = |w·x| + b
Answer: A
Rationale: The linear SVM decision function is f(x) = w·x + b, where w is the weight vector
and b is the bias term. The sign of f(x) determines the class prediction.
Q6: What is the hinge loss function?
A) L(y, f(x)) = max(0, 1 - y·f(x))
B) L(y, f(x)) = (y - f(x))²
C) L(y, f(x)) = |y - f(x)|
D) L(y, f(x)) = -log(1 + exp(-y·f(x)))
Answer: A
Rationale: Hinge loss is defined as max(0, 1 - y·f(x)), where y ∈ {-1, +1}. It penalizes
predictions that are on the wrong side of the margin, with no penalty for correct
predictions beyond the margin.
Q7: What does the parameter C control in SVM?
A) The learning rate
B) The trade-off between margin maximization and misclassification penalty
C) The number of support vectors
D) The kernel type
, Answer: B
Rationale: C is the regularization parameter that controls the trade-off between having a
wider margin and minimizing training error. Smaller C allows more misclassifications
(wider margin), larger C forces fewer misclassifications (narrower margin).
Q8: What happens when C approaches infinity in SVM?
A) The model becomes fully regularized
B) The model becomes a hard-margin SVM
C) The model ignores all training data
D) The model becomes a soft-margin SVM with maximum margin
Answer: B
Rationale: As C → ∞, the penalty for misclassification becomes infinitely large, forcing the
model to correctly classify all training points, effectively becoming a hard-margin SVM.
Q9: What happens when C approaches 0 in SVM?
A) The model becomes a hard-margin SVM
B) The model prioritizes margin maximization over classification accuracy
C) The model overfits the training data
D) The model becomes identical to logistic regression
Answer: B
Rationale: Small C values prioritize maximizing the margin even at the cost of
misclassifying some training points, leading to a simpler, more regularized model.
