Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was reading this paper related to adaptive multi-hyperplane machine for non linear classification

In that paper, they have mentioned about multiclass SVM, with multiple weights for each class.

The loss for any classification is

$l(x_n,y_n) = max_{i\epsilon y\\\y_n}(0,1 + max g(i,x_n) - g(y_n,x_n))$

where $y_n$ is the label for the nth example and $x_n$ is the features.

I have this confusion when they do the training of this algorithm. They call this SVM MM(Multiple Hyperplane).

They say the convex-approximated problem is defined as

$min_{W}P(W|z) = \frac{\lambda}{2}||W||^2 + \frac{1}{N}\sum_{n=1}^{N}l_{cvx}(W;(x_n,y_n);z_n)$

where they have the concave term $-g(y_n,z_n)$ replaced with the convex term $-w^T_{y_n,z_n}x_n$.

I am not sure if I have described it clearly. But I am going to attach the screenshot of the paper as well. The thing is I didn't get what's the difference between $-g(y_n,z_n)$ and $-w^T_{y_n,z_n}x_n$. They seem the same term to me.

I might be asking a lot. But can anyone provide some info?

enter image description here enter image description here

I have marked by the red rectangle the part that I didn't understand. I might be asking a lot. But I didn't get that part. Why is it so?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.