如何理解SVM中的功能裕度? [英] How to understand the functional margin in SVM ?

问题描述

我正在阅读Andrew NG的机器学习笔记，但是功能边距定义使我感到困惑:

I'm reading Andrew NG's Machine Learning notes, but the functional margin definition confused me :

我可以理解到几何裕度是x到其超平面的距离，但是如何理解功能裕度呢?为什么他们要这样定义其公式?

I can understand to geometric margin is the distance from x to its hyperplane, but how to understand functional margin ? And why they define its formula like that ?

推荐答案

这样想:w ^ T.x_i + b是模型对第i个数据点的预测. Y_i是它的标签.如果预测和地面真相具有相同的符号，则gamma_i将为正.此实例在类边界的内部"越远，gamma_i就会越大:这是更好的方法，因为将所有i加总起来，您的类之间将有更大的间隔.如果预测和标签在符号上不一致，则此数量将为负(预测者的错误决定)，这将减少您的保证金，并且您越不正确，该数量将减少得更多(类似于松弛变量) .

Think of it like this: w^T.x_i +b is the model's prediction for the i-th data point. Y_i is its label. If the prediction and ground truth have the same sign, then gamma_i will be positive. The further "inside" the class boundary this instance is, the bigger gamma_i will be : this is better because, summed over all i, you will have greater separation between your classes. If the prediction and the label don't agree in sign, then this quantity will be negative (incorrect decision by the predictor), which will reduce your margin, and it will be reduced more the more incorrect you are (analogous to slack variables).

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