Support Vector Machines: Hype or Hallelujah? - what is alfa?

Question

I at the moment trying to understand how SVM works with the help of this paper

The paper itself explains things pretty well, but there is an alfa term, which doesn't seem to be documented anywhere? could any of elaborate on what it means? and what effect it has?

The alfa terms is first seen in equation (1)

Answer 1

$c$ (resp. $d$) is a point on the convex hull of the points in Class 1 (resp. Class 2). Therefore, $c$ (resp. $d$) can be represented as a convex combination of the points in Class 1 (resp. Class 2). More specifically, $$ c = \sum_{y_i \in \text{ Class 1}} \alpha_i x_i\quad \text{ for some }\quad \sum_{y_i \in \text{ Class 1}}\alpha_i = 1\quad \text{ and } \quad \alpha_i \geq 0 $$ and $$ d = \sum_{y_i \in \text{ Class 2}} \alpha_i x_i\quad \text{ for some }\quad \sum_{y_i \in \text{ Class 2}}\alpha_i = 1\quad \text{ and } \quad \alpha_i \geq 0 $$

Answer 2

$\alpha$ is the vector of coefficients $\alpha_i$. The goal of the quadratic program is to find the vector $\alpha$ (and thus the coefficients $\alpha_i$) satisfying the constraints which minimize the quantity.