CS 559 Quiz 2: Linear Classification
Exam with verified answers and
rationale updated 2026
1. What is the primary goal of a linear classifier?
A) To minimize the number of features
B) To find a linear decision boundary that separates classes
C) To maximize the number of support vectors
D) To cluster unlabeled data
Answer: B
Rationale: Linear classifiers aim to find a hyperplane (linear decision boundary) that separates data
points belonging to different classes.
2. In a 2D feature space, what does a linear decision boundary look like?
A) A curve
B) A circle
C) A straight line
D) A point
Answer: C
Rationale: In 2D space, a linear decision boundary is represented by a straight line: w1x1 + w2x2 + b
= 0.
3. What is the general form of a linear discriminant function?
A) f(x) = wx² + b
B) f(x) = w^T x + b
C) f(x) = e^(wx+b)
D) f(x) = sin(wx)
,Answer: B
Rationale: The linear discriminant function is a weighted sum of input features plus a bias term.
4. What does the sign of w^T x + b determine in binary classification?
A) The magnitude of the feature vector
B) The class label
C) The learning rate
D) The number of iterations
Answer: B
Rationale: The sign of the discriminant function output determines which side of the decision
boundary the point falls on, corresponding to the predicted class.
5. What is the perceptron algorithm used for?
A) Clustering data
B) Finding linear decision boundaries through iterative weight updates
C) Dimensionality reduction
D) Regression analysis
Answer: B
Rationale: The perceptron is an iterative algorithm that updates weights based on misclassified
examples to find a linear separator.
6. In the perceptron learning rule, when are weights updated?
A) After every single example, regardless of classification
B) Only when a data point is misclassified
C) Never, weights are fixed
D) Only at the end of each epoch
Answer: B
Rationale: The perceptron only updates weights when a prediction error occurs, moving the
boundary to correctly classify the misclassified point.
,7. What is the perceptron update rule for weights?
A) w = w - η∇L
B) w = w + η(y - ŷ)x
C) w = w * η
D) w = w / η
Answer: B
Rationale: The perceptron update rule adjusts weights in the direction that reduces the classification
error, scaled by learning rate η.
8. What happens if data is not linearly separable when using the perceptron algorithm?
A) It converges immediately
B) It may never converge
C) It automatically switches to a nonlinear method
D) It produces perfect classification
Answer: B
Rationale: The perceptron convergence theorem guarantees convergence only for linearly separable
data; otherwise, it may oscillate indefinitely.
9. What is the margin in the context of linear classifiers?
A) The error rate of the classifier
B) The distance between the decision boundary and the nearest data points
C) The number of features used
D) The learning rate value
Answer: B
Rationale: The margin is the distance from the decision boundary to the closest data points, which is
maximized in SVMs.
10. What is the primary objective of a Support Vector Machine (SVM)?
, A) Minimize the number of support vectors
B) Maximize the margin between classes
C) Minimize the number of features
D) Maximize the training error
Answer: B
Rationale: SVM aims to find the hyperplane that maximizes the margin between the closest points of
different classes.
11. What are support vectors?
A) All data points in the training set
B) Only the misclassified points
C) Data points closest to the decision boundary that influence its position
D) The mean of each class
Answer: C
Rationale: Support vectors are the critical elements of the training set that lie closest to the decision
boundary and determine the optimal hyperplane.
12. In SVM, what is the role of the parameter C?
A) It controls the learning rate
B) It controls the trade-off between margin maximization and classification error
C) It determines the number of support vectors directly
D) It sets the number of iterations
Answer: B
Rationale: C is a regularization parameter that balances maximizing the margin against minimizing
classification errors (slack variables).
13. A high value of C in SVM leads to:
A) A wider margin with more misclassifications allowed
B) A narrower margin with less tolerance for misclassification
Exam with verified answers and
rationale updated 2026
1. What is the primary goal of a linear classifier?
A) To minimize the number of features
B) To find a linear decision boundary that separates classes
C) To maximize the number of support vectors
D) To cluster unlabeled data
Answer: B
Rationale: Linear classifiers aim to find a hyperplane (linear decision boundary) that separates data
points belonging to different classes.
2. In a 2D feature space, what does a linear decision boundary look like?
A) A curve
B) A circle
C) A straight line
D) A point
Answer: C
Rationale: In 2D space, a linear decision boundary is represented by a straight line: w1x1 + w2x2 + b
= 0.
3. What is the general form of a linear discriminant function?
A) f(x) = wx² + b
B) f(x) = w^T x + b
C) f(x) = e^(wx+b)
D) f(x) = sin(wx)
,Answer: B
Rationale: The linear discriminant function is a weighted sum of input features plus a bias term.
4. What does the sign of w^T x + b determine in binary classification?
A) The magnitude of the feature vector
B) The class label
C) The learning rate
D) The number of iterations
Answer: B
Rationale: The sign of the discriminant function output determines which side of the decision
boundary the point falls on, corresponding to the predicted class.
5. What is the perceptron algorithm used for?
A) Clustering data
B) Finding linear decision boundaries through iterative weight updates
C) Dimensionality reduction
D) Regression analysis
Answer: B
Rationale: The perceptron is an iterative algorithm that updates weights based on misclassified
examples to find a linear separator.
6. In the perceptron learning rule, when are weights updated?
A) After every single example, regardless of classification
B) Only when a data point is misclassified
C) Never, weights are fixed
D) Only at the end of each epoch
Answer: B
Rationale: The perceptron only updates weights when a prediction error occurs, moving the
boundary to correctly classify the misclassified point.
,7. What is the perceptron update rule for weights?
A) w = w - η∇L
B) w = w + η(y - ŷ)x
C) w = w * η
D) w = w / η
Answer: B
Rationale: The perceptron update rule adjusts weights in the direction that reduces the classification
error, scaled by learning rate η.
8. What happens if data is not linearly separable when using the perceptron algorithm?
A) It converges immediately
B) It may never converge
C) It automatically switches to a nonlinear method
D) It produces perfect classification
Answer: B
Rationale: The perceptron convergence theorem guarantees convergence only for linearly separable
data; otherwise, it may oscillate indefinitely.
9. What is the margin in the context of linear classifiers?
A) The error rate of the classifier
B) The distance between the decision boundary and the nearest data points
C) The number of features used
D) The learning rate value
Answer: B
Rationale: The margin is the distance from the decision boundary to the closest data points, which is
maximized in SVMs.
10. What is the primary objective of a Support Vector Machine (SVM)?
, A) Minimize the number of support vectors
B) Maximize the margin between classes
C) Minimize the number of features
D) Maximize the training error
Answer: B
Rationale: SVM aims to find the hyperplane that maximizes the margin between the closest points of
different classes.
11. What are support vectors?
A) All data points in the training set
B) Only the misclassified points
C) Data points closest to the decision boundary that influence its position
D) The mean of each class
Answer: C
Rationale: Support vectors are the critical elements of the training set that lie closest to the decision
boundary and determine the optimal hyperplane.
12. In SVM, what is the role of the parameter C?
A) It controls the learning rate
B) It controls the trade-off between margin maximization and classification error
C) It determines the number of support vectors directly
D) It sets the number of iterations
Answer: B
Rationale: C is a regularization parameter that balances maximizing the margin against minimizing
classification errors (slack variables).
13. A high value of C in SVM leads to:
A) A wider margin with more misclassifications allowed
B) A narrower margin with less tolerance for misclassification
