svm缩放输入值 [英] svm scaling input values

问题描述

我使用libSVM。
说明我的特征值格式如下：

I am using libSVM. Say my feature values are in the following format:

                         instance1 : f11, f12, f13, f14
                         instance2 : f21, f22, f23, f24
                         instance3 : f31, f32, f33, f34
                         instance4 : f41, f42, f43, f44
                         ..............................
                         instanceN : fN1, fN2, fN3, fN4

我认为可以应用两种缩放。

I think there are two scaling can be applied.

1. 向量，使得每个向量具有零均值和单位方差。

1. scale each instance vector such that each vector has zero mean and unit variance.

    ( (f11, f12, f13, f14) - mean((f11, f12, f13, f14) ). /std((f11, f12, f13, f14) )

将上述矩阵的每个列缩放到一个范围，例如[-1,1]

scale each colum of the above matrix to a range. for example [-1, 1]

根据我对RBF内核（libSVM）的实验，我发现第二次缩放（2）将结果提高约10％。我不明白为什么（2）给我一个改进的结果的原因。

According to my experiments with RBF kernel (libSVM) I found that the second scaling (2) improves the results by about 10%. I did not understand the reason why (2) gives me a improved results.

任何人可以解释我什么是应用缩放的原因，为什么第二个选项给我改进结果？

Could anybody explain me what is the reason for applying scaling and why the second option gives me improved results?

推荐答案

标准的做法是让每个维度（或属性或列零均值和单位方差。

The standard thing to do is to make each dimension (or attribute, or column (in your example)) have zero mean and unit variance.

这使SVM的每个维度都具有相同的大小。从 http://www.csie.ntu.edu.tw/~cjlin/papers /guide/guide.pdf ：

This brings each dimension of the SVM into the same magnitude. From http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf:

缩放的主要优点是避免更大数字的属性
范围主导那些在较小数字范围。另一个优点是在计算期间避免
数值困难。因为内核值通常取决于
特征向量的内积，例如。线性核和多项式ker-
nel，大的属性值可能会导致数值问题。我们建议线性
将每个属性缩放到范围[-1，+ 1]或[0,1]。

The main advantage of scaling is to avoid attributes in greater numeric ranges dominating those in smaller numeric ranges. Another advantage is to avoid numerical diculties during the calculation. Because kernel values usually depend on the inner products of feature vectors, e.g. the linear kernel and the polynomial ker- nel, large attribute values might cause numerical problems. We recommend linearly scaling each attribute to the range [-1,+1] or [0,1].

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