※ 引述《mengjia (try it)》之銘言：
: ※ 引述《hometoofar (家太遠了)》之銘言：
: : I tried to do the primal with slack variables starting by using the 4 points
: : to get 4 equations of w1, w2, b and the slack variable.
: : I did some algebra to reduce the equations but I can't get anything that's
: : really helpful. However I did notice something interesting..
: : If I just add the 4 equations, it shows that sum of the 4 slack variable >= 4
: : Then I just throw in w1=0, w2=0 and hope to find some b that works with the
: : slack variable constraint. A value of b exists so that w1=0 and w2=0 and sum
: : of slack variable = 4. I believe that it minimizes the equation.. but there
: : are two things I am concering about...
: : 1. This is not a good mathematical way... I can't just random pick some number
: : and claim it to be the optimal.
: : 2. What line does w=[0 0]T give? I know that this dataset is not linearly
: : separatable unless I have a >1 slack variable for one of the o or x point,
: : but I can at least draw such a line. The idea of w=[0 0]T doesn't make me
: : feel right.
: I think of solving the primal "without" slack variables.
: If using slack variables, we can't match the dual.
: (Of course, I first assume no advanced dual solution exists.)
: Because the example is not separable, the primal is not solvable.
I don't think so.
if we add a penalty term, the primal should be solvable.
I think the mengjia's solution may be correct.
this is the only way I can get a solution.
: : Also I am stuck on dual too...
: : I get the alpha equation, but I don't know how to find the values of alphas.
: : I get the equation, I get the constraint that yTa = 0, but there are 4
: : unknown alphas..
: : Again, I try to make everything 0, simple, but I know it isn't good.
: : (Like the page 23 example of lecture notes, set alpha1=0 meet the constraints,
: : but it's not the right solution)
: : I tried to find another set of alpha that aren't all 0 and minimize the
: : equation, but that set gives me really big w...
: For dual, I can compute alpha. I just say it needs a trick,too. = =+
: Alpha is a zero column.
I also get the sol of alpha, but I don't use any special trick!! @_@
Just an algebra computation
and I get a different sol with yours.
but my sol could match the primal-dual relationship.