问题
I am currently working on a support vector machine (SVM) project. The version of SVM that I am working on is Linear SVM in Primal Form and I am having hard time understanding where to start.
In general, I think I understand the theory; basically I need to minimize norm of w under certain constraint. And the Lagrangian function will be my objective function to be minimized (after Lagrange multiplier is applied).
The things that I don't understand is that I was told from my professor that we will be using Quasi-Newton method along with BFGS update. I have tried 2D and 3D case for Newton's method and I think I have good grasp of the algorithm, but I don't see how Quasi-Newton method is applied to find the coefficients alpha. Also, many literature that I read so far tells to apply Quadratic programming to find the coefficients.
How is the iterative algorithm of Quasi-Newton related to finding coefficients of w...? And how is quadratic programming related to Quasi-Newton? Can anyone please walk me through what is going on?
回答1:
You are cunfusing many things here
- "alpha coefficients" are only in the dual form, so you do not find them in your case
- "apply Quadratic programming", quadratic programming is a problem, not a solution. you cannot "apply QP", you can only solve a QP, which in your case will be solved using quasi-newton method
- "how is (...) related to finding coefficientss of w" exactly the same way, as this optimization technique is related to finding the optimal coefficients of any function. You are going to minimize the function of w, so applying any optimization technique (in particular quasi-netwton) will lead to solution expressed as w coefficients
来源：https://stackoverflow.com/questions/23752856/support-vector-machine-primal-form-implementation