问题

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.

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

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).

Here are the methods that I've tried:

1 Looping method:

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 Vectorized Method

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

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!

Any help would be appreciated.

回答1:

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

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).

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.

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.

To conclude, I misunderstood how pipelines worked.

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)

Addendum

For those who are interested in implementing a manual method for a multiclass SVC, the following link is helpful: https://stackoverflow.com/a/27752709/1182556

来源：https://stackoverflow.com/questions/28503932/calculating-decision-function-of-svm-manually

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python