Math Problem Statement

ans

For a two class problem shown in figure, classify the unknown point (5, 2.5) using SVM?

Solution

To classify the point (5,2.5)(5, 2.5) using a Support Vector Machine (SVM), we analyze the diagram provided.

  • Class 1 points are marked in red.
  • Class 2 points are marked in blue.
  • The goal is to classify the unknown point using an SVM decision boundary, which separates the two classes.

Looking at the graph, the point (5,2.5)(5, 2.5) lies in the middle region, closer to the cluster of red points (Class 1), but also not far from the blue points (Class 2). However, it appears to be more aligned with Class 1 points, suggesting that an SVM decision boundary would likely classify it as Class 1.

Thus, the correct answer would likely be:

a) Class 1

Would you like more details about SVM or decision boundaries?

Here are 5 related questions:

  1. How does SVM determine the optimal decision boundary between two classes?
  2. Can SVM handle non-linear separations, and how does it do so?
  3. What role do support vectors play in SVM classification?
  4. How does the distance from the boundary affect the classification decision?
  5. What are some real-world applications of SVM?

Tip: In SVM, maximizing the margin between the decision boundary and the closest points from both classes ensures robustness in classification.

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Math Problem Analysis

Mathematical Concepts

Support Vector Machines (SVM)
Binary Classification
Decision Boundaries

Formulas

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Theorems

Support Vector Theorem
Margin Optimization in SVM

Suitable Grade Level

Undergraduate