To determine the correct set of support vectors for an SVM classifier from the provided two-class data distribution:

1. Identify the Classes:

   • Class 1 is represented by red points.
   • Class 2 is represented by blue points.

2. Support Vectors:

   • Support vectors are the points from each class that are closest to the decision boundary between the two classes. These points essentially "support" the boundary by being the closest points to it, and they are crucial in defining the SVM's margin.

3. Observing the Figure:

   • The decision boundary will likely pass through the middle region, where the clusters are most separated vertically.
   • The support vectors will be points close to the opposite sides of this boundary, from each class.

4. Potential Support Vectors:

   • For Class 1 (red), the likely support vectors are:
     • Points near $(4, 2)$ and $(2, 3)$.
   • For Class 2 (blue), the likely support vectors are:
     • Points near $(5, 5)$ and $(6, 3)$.

These points are the closest to the hypothetical decision boundary for this distribution, so they are probable candidates for support vectors in the SVM classifier.

Would you like further details on SVM margin calculations, or have any other questions?

Relative Questions:

1. How do support vectors affect the SVM classifier's decision boundary?
2. What role does the margin play in an SVM classifier, and how is it defined?
3. How can we use kernel functions with SVMs to separate non-linearly separable data?
4. Why might SVMs be preferable in situations with high-dimensional data?
5. How does the choice of C parameter in SVM affect the classifier’s behavior?

Tip:

In SVMs, maximizing the margin between classes generally improves the model’s generalizability by reducing overfitting, especially in cases with small amounts of training data.