自定义 SVM 多项式内核 sklearn

Question

我被要求为 SVM 开发一个自定义多项式（度数 = 3,4,5）内核，并将其精度与 sklearnkit 的内置多内核进行比较（应该几乎相同） 我尝试遵循多项式内核定义，但我的结果似乎不太相似，这是我的代码：

def poly_kernel_fn(X, Y):
# Implement a polynomial kernel
#  - args: 2 numpy arrays of shape [n_samples, n_features]
#  - returns: computed kernel matrix of shape [n_samples, n_samples]

K = np.zeros((X.shape[0],Y.shape[0]))
K = (X.dot(Y.T) + 1)**4
return K

clfpoly = svm.SVC(kernel='poly', degree=4)
clfpoly.fit(X_train, y_train)
zpoly = clfpoly.predict(X_test)
print("The accuracy with in-built 3D polynomial kernel is: ",accuracy_score(y_test, zpoly)*100,"%")

clf = svm.SVC(kernel=poly_kernel_fn)
clf.fit(X_train, y_train)
z = clf.predict(X_test)
print("The accuracy with custom rbf kernel is: ",accuracy_score(y_test, z)*100,"%")

准确率结果如下：

• 内置 4D 多项式内核的精度为：56.99999999999999 %
• 使用内核的准确率是：59.0 %

如果我将多项式等级更改为 3 或 5，它的变化会更大，所以我不知道我做错了什么，或者根本无法匹配内置精度。

感谢您的帮助

Answer 1

你得看一下poly case的定义

https://scikit-learn.org/stable/modules/svm.html#svm-kernels

coef = 0 和 gamma = 1/(n_features*.var()) 然后你就可以得到相同的

from sklearn.datasets import make_classification
from sklearn import svm
import numpy as np

gamma = None
   
def poly_kernel_fn(X, Y):
   
   K = np.zeros((X.shape[0],Y.shape[0]))
   K = (gamma*X.dot(Y.T))**4
   return K
   
   

if __name__=="__main__":
    
    X, Y = make_classification(10, 5)  # random data
    
    clf1 = svm.SVC(kernel='poly', degree=4) # built in function
    
    clf1.fit(X, Y)
    print("built in score  = ", clf1.score(X,Y))
    
    gamma = 1/(5*X.var())
    
    clf2 = svm.SVC(kernel=poly_kernel_fn)
    
    clf2.fit(X, Y)
    print("custom in score = ", clf2.score(X,Y))

In [9]: run main.py
built in score  =  0.8
custom in score =  0.8