支持向量机原始形式的实现 [英] Support Vector Machine Primal Form Implementation

问题描述

我目前正在研究支持向量机(SVM)项目.我正在使用的SVM版本是原始形式的线性SVM ，很难理解从哪里开始.

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.

总的来说，我认为我理解理论.基本上，我需要在一定约束下最小化w的范数.拉格朗日函数将是我要最小化的目标函数(应用拉格朗日乘数后).

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).

我不了解的是，我的教授告诉我，我们将同时使用准牛顿法和BFGS更新.我已经尝试了牛顿法的2D和3D情况，并且我对算法有很好的掌握，但是我看不到如何应用准牛顿法来找到系数α.而且，到目前为止，我读过的许多文献都讲要应用二次编程来找到系数.

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.

拟牛顿迭代算法与找到w ...的系数有什么关系?二次编程与拟牛顿有何关系?谁能告诉我发生了什么事?

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?

推荐答案

您在这里混淆了许多事情

You are cunfusing many things here

• "alpha系数" 仅采用对偶形式，因此您找不到这种情况
• 应用二次编程"，二次编程是一个问题，不是解决方案.您不能应用QP"，只能解决一个QP，在您的情况下，将使用准牛顿法解决该问题
• (...)如何与找到w的系数相关"完全相同，因为此优化技术与找到任何函数的最佳系数有关.您将使w的函数最小化，因此应用任何优化技术(尤其是拟网域)将导致以 w 系数表示的解

• "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

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