1. When you say "standard SVM with binary classification" you mean: **min 0.5||w||^2 + C \sum_{i=1}_{m} max(0, 1-y_i*<w,x_I>)**

2. Hi, if I understand correctly the question I need to find w* as function of w_1* and w_2* . And after that to prove than the w* I found minimizing the standard SVM problem.

(something doesn't work to me with the algebra so I just want to make sure that I understand the question)

Correct?

1. It's the formulation in 3(a).

2. You need to show the correspondence between the two solutions (e.g., how you get from one to another, and the other way around), and why do you get the same classifier. You can achieve the goal in whatever means you see fit.

Can we assume that the correspondence occures for different C's? Since the penalty coefficient C is relative to the coefficient of the squared norms (i.e. ||w||^2)

Thanks!

If you don't get that it's the same, but you have a solid argument how to map the different C's, this is fine.

but am I in the right direction? or is there a way to show that the specific correspondence between w* and w_1*, w_2* holds without making such assumption (same C for both problems)?

I think I found a counter example to the fact that w1*,w2* and w* correspond with the same C.

is it possible that there is a mistake in this subsection and the correspondence occurs only when the C of the multiclass svm equals to 0.5 times C of the standard svm?

the counter example: m=1 d=1 x_1 = 1 y_1 = 2 (-1 in binary but can also be the opposite) and C = 1 for both or C = 0.1 for both (the two C's give different correspondences)

Maybe. I think you have all the information you need to solve this problem.