手动计算支持向量机的决策函数 [英] Calculating decision function of SVM manually

问题描述

我正在尝试使用python库SKLearn手动(与使用内置方法相对)计算SVC分类器的Decision_function.

I'm attempting to calculate the decision_function of a SVC classifier MANUALLY (as opposed to using the inbuilt method) using the the python library SKLearn.

我尝试了几种方法，但是，只有在不缩放数据时，我才能获得与之匹配的手动计算.

I've tried several methods, however, I can only ever get the manual calculation to match when I don't scale my data.

z是一个测试数据(已按比例缩放)，我认为其他变量可以说明一切(此外，如果代码中不明显，我将使用rbf内核).

z is a test datum (that's been scaled) and I think the other variables speak for themselves (also, I'm using an rbf kernel if thats not obvious from the code).

以下是我尝试过的方法:

Here are the methods that I've tried:

dec_func = 0
for j in range(np.shape(sup_vecs)[0]):

    norm2 = np.linalg.norm(sup_vecs[j, :] - z)**2 
    dec_func = dec_func + dual_coefs[0, j] * np.exp(-gamma*norm2)

dec_func += intercept

2矢量化方法

diff = sup_vecs - z
norm2 = np.sum(np.sqrt(diff*diff), 1)**2
dec_func = dual_coefs.dot(np.exp(-gamma_params*norm2)) + intercept

但是，它们都不返回与decision_function相同的值.我认为这可能与重新调整我的价值观有关，或者更有可能是我一直在寻找的愚蠢事物！

However, neither of these ever returns the same value as decision_function. I think it may have something to do with rescaling my values or more likely its something silly that I've been over looking!

任何帮助将不胜感激.

推荐答案

因此，在进行更多挖掘和抓挠之后，我已经弄清楚了.

So after a bit more digging and head scratching, I've figured it out.

如上所述，z是已缩放的测试数据.要进行缩放，我必须从preprocessing.StandardScaler()对象中提取.mean_和.std_属性(当然是在训练数据上调用.fit()之后).

As I mentioned above z is a test datum that's been scaled. To scale it I had to extract .mean_ and .std_ attributes from the preprocessing.StandardScaler() object (after calling .fit() on my training data of course).

然后我将缩放后的z用作我的手动计算和内置函数的输入.但是，内置函数是管道的一部分，该管道已经将StandardScaler作为其管道中的第一个管道"，结果z被缩放了两次！ 因此，当我从管道中删除缩放比例时，手册回答匹配"了内置函数的回答.

I was then using this scaled z as an input to both my manual calculations and to the inbuilt function. However the inbuilt function was a part of a pipeline which already had StandardScaler as its first 'pipe' in the pipeline and as a result z was getting scaled twice! Hence, when I removed scaling from my pipeline, the manual answers "matched" the inbuilt function's answer.

我用引号说匹配"，因为我总是不得不翻转手动计算的符号以匹配内置版本.目前我不知道为什么会这样.

I say "matched" in quotes by the way as I found I always had to flip the sign of my manual calculations to match the inbuilt version. Currently I have no idea why this is the case.

最后，我误解了管道的工作原理.

To conclude, I misunderstood how pipelines worked.

对于那些感兴趣的人，这是我的手动方法的最终版本:

For those that are interested, here's the final versions of my manual methods:

diff = sup_vecs - z_scaled
# Looping Method
dec_func_loop = 0
for j in range(np.shape(sup_vecs)[0]):
    norm2 = np.linalg.norm(diff[j,:]) 
    dec_func_loop = dec_func_loop + dual_coefs[j] * np.exp(-gamma*(norm2**2))

dec_func_loop = -1 * (dec_func_loop - intercept)

# Vectorized method
norm2 = np.array([np.linalg.norm(diff[n, :]) for n in range(np.shape(sup_vecs)[0])])
dec_func_vec = -1 * (dual_coefs.dot(np.exp(-gamma*(norm2**2))) - intercept)

附录

对于那些对实现多类SVC的手动方法感兴趣的人，以下链接会有所帮助: https://stackoverflow. com/a/27752709/1182556

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