Pattern Recognition Lecture 3: Classification I Quiz

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Questions and Answers

What is the main purpose of using Support Vector Machines (SVMs) for classification?

To reduce the dimensionality of the feature space and improve computational efficiency.

To perform logistic regression and find the decision boundary between the classes.

To minimize the cost function and find the optimal hyperplane that separates the classes with the maximum margin. (correct)

To cluster the data points into different groups based on their similarity.

What is the difference between the cost function used in logistic regression and the cost function used in SVMs?

Logistic regression has a regularization term, while SVMs do not have a regularization term.

Logistic regression minimizes the sum of squared errors, while SVMs minimize the sum of absolute errors.

Logistic regression considers the distance of each data point from the decision boundary, while SVMs consider only the distance of the support vectors.

Logistic regression uses the log-loss function, while SVMs use the hinge-loss function. (correct)

What is the significance of the margin in SVMs?

The margin determines the complexity of the decision boundary, with a larger margin leading to a simpler decision boundary.

The margin is used to compute the regularization term in the SVM cost function.

The margin is the distance between the decision boundary and the closest data points, and maximizing the margin leads to better generalization. (correct)

The margin is used to determine the number of support vectors, which in turn determines the computational complexity of the SVM.

What is the role of the support vectors in SVMs?

Support vectors are the data points that lie on the margin of the decision boundary and determine its shape and position. Signup and view all the answers

How does the choice of the regularization parameter $C$ in SVMs affect the learning process and the resulting classifier?

A larger value of $C$ leads to a more complex decision boundary with a smaller margin, while a smaller value of $C$ leads to a simpler decision boundary with a larger margin. Signup and view all the answers

How do the decision boundaries of logistic regression and SVMs differ?

Logistic regression finds a decision boundary that minimizes the sum of squared errors, while SVMs find a decision boundary that maximizes the margin between the classes. Signup and view all the answers

Logistic regression and SVMs both use hinge loss as their cost function.

False Signup and view all the answers

Support Vector Machines (SVMs) maximize the margin between the decision boundary and the support vectors.

True Signup and view all the answers

In SVMs, the support vectors are the training points that lie outside the margin.

False Signup and view all the answers

The regularizer parameter in SVMs, denoted as C, is inversely proportional to lambda (λ).

True Signup and view all the answers

The alternative view of logistic regression focuses on minimizing the hinge loss function.

False Signup and view all the answers

Support vectors in SVMs solely determine the position of the decision boundary.

False Signup and view all the answers

Study Notes

Classification I

Support Vector Machines (SVMs) are an alternative view of logistic regression.

Cost Function

Cost of example: If (want 1), hinge-loss is applied.
If (want -1), hinge-loss is also applied.

Support Vector Machine

SVM: min 1/m * Σ [y^(i) * cost1 * θ^T * x_i + (1 - y_i) * cost0 * θ^T * x_i] + λ/2 * Σ θ_j^2
By removing 1/m, and multiplying by 1/λ, let C = 1/λ.
SVM: min [Σ y^(i) * cost1 * θ^T * x_i + (1 - y_i) * cost0 * θ^T * x_i] + C/2 * Σ θ_j^2

Logistic Regression vs. Support Vector Machine

Logistic Regression: θ^T * x ≤ -1 or θ^T * x ≥ 1
Support Vector Machine: θ^T * x = 0

Margin and Support Vectors

Margin: The distance between the hyperplane and the closest data points.
Support vectors:
- They are the training points that define the maximum margin of the hyperplane to the data set.
- They determine the shape (position & orientation) of the hyperplane.
Support vectors properties: They are the points that lie closest to the hyperplane.

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Description

Test your understanding of Classification (SVM), Cost Function, Support Vector Machines, and Alternative views of logistic regression from Lecture 3 of the Pattern Recognition course by Dr. Dina Khattab at Faculty of Computer & Information Sciences, Ain Shams University.

Pattern Recognition Lecture 3: Classification I Quiz

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Questions and Answers

What is the main purpose of using Support Vector Machines (SVMs) for classification?

What is the difference between the cost function used in logistic regression and the cost function used in SVMs?

What is the significance of the margin in SVMs?

What is the role of the support vectors in SVMs?

How does the choice of the regularization parameter $C$ in SVMs affect the learning process and the resulting classifier?

How do the decision boundaries of logistic regression and SVMs differ?

Logistic regression and SVMs both use hinge loss as their cost function.

Support Vector Machines (SVMs) maximize the margin between the decision boundary and the support vectors.

In SVMs, the support vectors are the training points that lie outside the margin.

The regularizer parameter in SVMs, denoted as C, is inversely proportional to lambda (λ).

The alternative view of logistic regression focuses on minimizing the hinge loss function.

Support vectors in SVMs solely determine the position of the decision boundary.

Study Notes

Classification I

Cost Function

Support Vector Machine

Logistic Regression vs. Support Vector Machine

Margin and Support Vectors

Studying That Suits You

Description

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