# Numerical example on Support Vector Machines

I was watching this numerical problem on SVM link here. At 4.42 he wrote this equation:

\begin{align} \alpha_1 \tilde{s_1} \cdot \tilde{s_1} + \alpha_2 \tilde{s_2} \cdot \tilde{s_1} + \alpha_3 \tilde{s_3} \cdot \tilde{s_1} &= -1 \\ \alpha_1 \tilde{s_1} \cdot \tilde{s_2} + \alpha_2 \tilde{s_2} \cdot \tilde{s_2} + \alpha_3 \tilde{s_3} \cdot \tilde{s_2} &= +1 \\ \alpha_1 \tilde{s_1} \cdot \tilde{s_3} + \alpha_2 \tilde{s_2} \cdot \tilde{s_3} + \alpha_3 \tilde{s_3} \cdot \tilde{s_3} &= +1 \end{align}

where $$\tilde{s_1}, \tilde{s_2}, \tilde{s_3}$$ are support vectors. But from the support vector we see that: $$w = \sum \alpha_i y_i s_i$$ where $$y_i$$ is class label and $$s_i$$ is support vector. Since $$\alpha$$'s are zero for all other points except support vector so I am considering only the support vector here. My question is if we look at the above equation he just wrote: $$w = \sum \alpha_i s_i$$

I can't understand how he wrote $$w = \sum \alpha_i s_i$$ and get the correct answer yet?

I dont think so. He wrote $$\sum_i \alpha_ix_i^Tx$$ where $$x$$ is the test sample. He took $$x$$ as each support vector and hence that summation will result to 1 or -1 (depending on class).