In this question you will implement kernel k$-$means with modified RBF$-$kernel, using SpectralClustering from sklearn to reduce the programming efford of the full implementation.

For reference, please write the formula of your RBF kernel as

$(x_i,x_j)=$exp$(\frac{-|x_i-x_j{|}_2^2}{m_2})$

In order to calculate pairwise distance matrix, please use scipy.spatial distance function, which is already pre$-$loaded in the code.

Please check the documentation of the SpectralClustering function on how to use precomputed affinity matrix, which you are going to supply with the above

specification.

import numpy as np

from sklearn.cluster import SpectralClustering

from scipy.spatial import distance

df $=$ pd$.$read$\_$csv$(\text{'}$train$1.$csv$\text{'},$ header $=$ None$)$

X $=$ df$.$iloc$[$:$1000,1$:$].$to$\_$numpy$($copy$=$True$)$

Y $=$ df$.$iloc$[$:$1000,$:$1].$to$\_$numpy$($copy$=$True$)$

n$\_$clusters $=10$

centroids$\_$rbf $=$ np$.$array$($n$\_$clusters$)$

centroids$\_$rbf $=[]$DO NOT use any other import statements for this question

$""""""$

print$(\text{'}$Sum of centroids:$\text{'})$

print$($np$.$round$($np$.$sum$($centroids$\_$rbf$),2))$

Note: Please do not use the answer of Chatgpt.