What exactly are support vectors?

What exactly are support vectors?

Support vectors are data points that are closer to the hyperplane and influence the position and orientation of the hyperplane. Using these support vectors, we maximize the margin of the classifier. Deleting the support vectors will change the position of the hyperplane. These are the points that help us build our SVM.

Can a support vector lie on the margin?

In the case of linearly separable data, the support vectors are those data points that lie (exactly) on the borders of the margins.

Do all support vectors have same margin?

They are not all equal. In the absence of slack variables (hard margin SVM), α values are not equal because α is a direct part of the objective function as shown in the first two equations.

When do you use a support vector classifier?

For such cases, a support vector classifier comes to the rescue. From the above diagram, we can assume infinite hyperplanes (left). The maximum margin classifier comes with a single hyperplane that divides the data (right). The data touching the positive and negative hyperplanes is referred to as support vectors.

What do you call a support vector machine?

This best decision boundary is called a hyperplane. SVM chooses the extreme points/vectors that help in creating the hyperplane. These extreme cases are called as support vectors, and hence algorithm is termed as Support Vector Machine.

What are the support vectors in a SVM?

In the case of linearly separable data, the support vectors are those data points that lie (exactly) on the borders of the margins. These are the only points that are necessary to compute the margin (through the bias term b ). For C-SVMs, however, I always get confused as to what exactly the support vectors are.

Why do we need so many support vectors?

Doing so could help you determine how separable your dataset is, to give just one example: if many support vectors are necessary, the model had more difficulty generating the boundary than when say, one vector on each side was used to find the boundary.