I am trying to understand the basics of SVM algebra, but fail to understand per below:

Let us formalize an SVM with algebra. A decision hyperplane can be defined by an intercept term $b$ and a decision hyperplane normal vector $\vec{w}$ which is perpendicular to the hyperplane. This vector is commonly referred to in the machine learning literature as the weight vector . To choose among all the hyperplanes that are perpendicular to the normal vector, we specify the intercept term $b$. Because the hyperplane is perpendicular to the normal vector, all points $\vec{x}$ on the hyperplane satisfy $\vec{w}^{T}\vec{x} = -b$.

can someone give me a pointer / hint to understand the last equation? is it linked to the fact that the cross-product of two perpendicular vectors should be zero? much appreciated


1 Answer 1


A line is a hyperplane in the 2-dimensional space. Think of your equation as an equation defining a line in your space (simple as that: $a\bullet x+b=0$). Now, you can see that your $w$-vector is the slope of your line/decision boundary and your equation is a way to create a good decision boundary between two classes in the 2-dimensional space. Think of $w$ as the force with which we can push the decision boundary to different directions.

It is true, as seem to already know, that $w\bullet x$ is the inner or scalar product defined as $w\bullet x = \sum_{i}{w_ix_i}$.

In the SVMs, we can say that the decision boundary is used by saying that any $x$ value that gives a positive result for $wx+b$, is above the line, and so it belongs to the '+' class, while any $x$ that gives a negative result is in the '-' class.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.