SVM-什么是功能裕度? [英] SVM - what is a functional margin?

问题描述

几何余量只是某个x(数据点)与超车道之间的欧式距离.

A geometric margin is simply the euclidean distance between a certain x (data point) to the hyperlane.

什么是功能性空白的直观解释?

What is the intuitive explanation to what a functional margin is?

注意:我意识到这里也有人问过类似的问题: 如何了解SVM中的功能裕量?

Note: I realize that a similar question has been asked here: How to understand the functional margin in SVM ?

但是，在那里给出的答案解释了该方程式，但没有解释其含义(据我所知).

However, the answer given there explains the equation, but not its meaning (as I understood it).

推荐答案

几何边界只是在某个x(数据点)与超车道之间的欧几里得距离."

"A geometric margin is simply the euclidean distance between a certain x (data point) to the hyperlane. "

我认为这不是对几何边距的正确定义，我相信那是让您感到困惑的地方.几何边距只是功能边距的缩放版本.

I don't think that is a proper definition for the geometric margin, and I believe that is what is confusing you. The geometric margin is just a scaled version of the functional margin.

您可以认为功能裕量就像测试功能一样，可以告诉您特定点是否已正确分类.几何边距是由|| w ||

You can think the functional margin, just as a testing function that will tell you whether a particular point is properly classified or not. And the geometric margin is functional margin scaled by ||w||

如果您检查公式:

您会注意到，与标签无关，对于正确分类的点(例如sig(1 * 5)= 1和sig(-1 * -5)= 1)，结果将为正；否则为负.如果按|| w ||缩放比例那么您将拥有几何边距.

You can notice that independently of the label, the result would be positive for properly classified points (e.g sig(1*5)=1 and sig(-1*-5)=1) and negative otherwise. If you scale that by ||w|| then you will have the geometric margin.

为什么几何边距存在?

要最大限度地增加余量，您需要的不仅仅是符号，还需要有幅度的概念，功能余量会给您一个数字，但是如果没有参考，您就无法分辨出该点实际上是在远处还是在远处靠近决策平面.几何边距不仅在告诉您点是否已正确分类，还告诉您该距离的大小，单位为| w |.

Well to maximize the margin you need more that just the sign, you need to have a notion of magnitude, the functional margin would give you a number but without a reference you can't tell if the point is actually far away or close to the decision plane. The geometric margin is telling you not only if the point is properly classified or not, but the magnitude of that distance in term of units of |w|

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