right now I am dealing with a topic from machine learning, binary classification. In my lecture notes we have a minimization problem:
$$ min_{w,b}|\{i\in\{1,\ldots,n\}\colon sign(w^Tx_i - b) = y_i\}| $$ and $$y_i\in\{1,-1\}$$
Now they argue that it isn't a good idea to solve this optimization problem since the direction and offset in $(w,b)$ doesn't matter for the objective function. Can someone clarify what is meant by the this? I mean of course the objective function is dependent on $(w,b)$?