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?

    <p>Support vectors are the data points that lie on the margin of the decision boundary and determine its shape and position.</p> 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?

    <p>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.</p> Signup and view all the answers

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

    <p>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.</p> Signup and view all the answers

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

    <p>False</p> Signup and view all the answers

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

    <p>True</p> Signup and view all the answers

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

    <p>False</p> Signup and view all the answers

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

    <p>True</p> Signup and view all the answers

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

    <p>False</p> Signup and view all the answers

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

    <p>False</p> 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.

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