如何获取scikit-learning SVM分类器的所有alpha值?

问题描述

在用scikit-learn训练了SVM分类器之后，我需要alpha值，这是SVM对偶问题的拉格朗日乘数.根据该文档，似乎scikit-learn仅提供svm.dual_coef_，这是拉格朗日乘数alpha与数据点标签的乘积.

I need the alpha values, which are the Lagrange multipliers of the SVM dual problem, after training a SVM classifier with scikit-learn. According to the document, it seems that scikit-learn provides only svm.dual_coef_, which is the product of the Lagrange multiplier alpha and the label of a data point.

我尝试通过将svm.dual_coef_的元素除以数据标签来手动计算alpha值，但是由于svm.dual_coef_仅存储支持向量的系数，因此我不确定是否对这个数组进行迭代，支持向量的顺序与原始训练数据中的顺序相同.

I tried to calculate the alpha value manually by dividing the elements of svm.dual_coef_ by the data label, but since svm.dual_coef_ stores only the coefficients of the support vectors, I'm not sure if I iterate over this array, the order of support vectors would be the same as the order in the original training data.

那么有没有一种可靠的方法来获取支持向量的alpha值?

So is there a reliable way to get the alpha values of support vectors?

推荐答案

由于alpha值按定义是正数，因此可以通过使用double_coefs来获取它:

As alpha values are by definition positive you can get it through taking abs of dual_coefs:

alphas = np.abs(svm.dual_coef_)

whis是以下事实的直接结果

whis is a direct consequence of the fact that

svm.dual_coef_[i] = labels[i] * alphas[i]

其中labels[i]是-1或+1，而alphas[i]始终为正.此外，您还可以通过获得每个标签

where labels[i] is either -1 or +1 and alphas[i] are always positive. Futhermore, you can also get each label through

labels = np.sign(svm.dual_coef_)

使用相同的观察结果.这也是为什么scikit-learn不会这样存储alpha的原因-它们由dual_coefs_以及标签唯一表示.

using the same observation. This is also why scikit-learn does not store alphas as such - they are uniquely represented by dual_coefs_, together with labels.

分析所有可能的情况后，很容易理解它:

It is easy to understand it once you analyze all possible cases:

• labels[i] == -1和alphas[i] > 0 => dual_coef_[i] < 0和dual_coef_[i] == -alphas[i] == labels[i] * alphas[i]
• labels[i] == -1和alphas[i] < 0 => 不可能(字母为非负数)
• labels[i] == -1和alphas[i]== 0 => 它不是支持向量
• labels[i] == +1和alphas[i] > 0 => dual_coef_[i] > 0和dual_coef_[i] == alphas[i] == labels[i] * alphas[i]
• labels[i] == +1和alphas[i] < 0 => 不可能(字母为非负数)
• labels[i] == +1和alphas[i]== 0 => 它不是支持向量

• labels[i] == -1 and alphas[i] > 0 => dual_coef_[i] < 0 and dual_coef_[i] == -alphas[i] == labels[i] * alphas[i]
• labels[i] == -1 and alphas[i] < 0 => impossible (alphas are non-negative)
• labels[i] == -1 and alphas[i]== 0 => it is not a support vector
• labels[i] == +1 and alphas[i] > 0 => dual_coef_[i] > 0 and dual_coef_[i] == alphas[i] == labels[i] * alphas[i]
• labels[i] == +1 and alphas[i] < 0 => impossible (alphas are non-negative)
• labels[i] == +1 and alphas[i]== 0 => it is not a support vector

因此，如果dual_coef_[i]为正，则它是alphas[i]系数，属于正类，如果dual_coef_[i]为负，则alphas[i] == -dual_coef_[i]属于负类.

Consequently, if dual_coef_[i] is positive then it is the alphas[i] coefficient, and it belongs to positive class, and if it is negative, alphas[i] == -dual_coef_[i] and it belongs to negative class.

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