Python Scikit Learn Metrics - Polynomial Kernel














































Python Scikit Learn Metrics - Polynomial Kernel



Introduction:


*It computes the degree-d polynomial kernel between two vectors.
*It represents the similarity between two vectors.
*It considers not only the similarity between vectors under the same dimension, but also across dimensions.
*It accounts for feature interaction in ML.



Parameter:

*X - array like structure.
*Y - array like structure.
*d - kernel degree(default value = 3).
*co - constant(default value = 1).
*gamma - 1/(no of features).




Returns:

*Returns the gram(kernel) matrix.



Implementation of Polynomial Kernel:


from math import *
import numpy as np


class PolKer:


  def ker_calc(self,l1,l2,n_features,co = 1,d = 3):
    
    ans = []
    gam = 1.0/n_features

    for i in range(len(l1)):
      
      x = []
      for j in range(len(l2)):

        y = ((gam * l1[i][0] * l2[j][0]) + co) ** d
        x.append(y)
        
      ans.append(x)

    print(ans)



def main():

  Po = PolKer()
  l1 = [[2],
        [4]]
  l2 = [[1],
        [6]]
  n_features = len(l1[0])

  Po.ker_calc(l1,l2,n_features)



if __name__=="__main__":
  main()





Output:


[[ 27. 2197.]
[ 125. 15625.]]





Using Inbuilt Library:


from sklearn.metrics.pairwise import polynomial_kernel
x=np.array([[2],
   [4]])
y=np.array([[1],
   [6]])
print(polynomial_kernel(x,y))



Output:


[[ 27. 2197.]
[ 125. 15625.]]






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