Rahul Bansal

step 6: Determine centers of the neurons using KMeans.

K_cent= 8

km= KMeans(n_clusters= K_cent, max_iter= 100)

km.fit(X_train)

cent= km.cluster_centers_

step 7: Determine the value of [latex]\sigma[/latex]

max=0 

for i in range(K_cent):

	for j in range(K_cent):

		d= numpy.linalg.norm(cent[i]-cent[j])

		if(d> max):

			max= d

d= max



sigma= d/math.sqrt(2*K_cent)

step 8: Set up matrix G.

shape= X_train.shape

row= shape[0]

column= K_cent

G= numpy.empty((row,column), dtype= float)

for i in range(row):

    for j in range(column):

        dist= numpy.linalg.norm(X_train[i]-cent[j])

        G[i][j]= math.exp(-math.pow(dist,2)/math.pow(2*sigma,2))

step 9: Find weight matrix W to train the network.

GTG= numpy.dot(G.T,G)

GTG_inv= numpy.linalg.inv(GTG)

fac= numpy.dot(GTG_inv,G.T)

W= numpy.dot(fac,Y_train)

step 10: Set up matrix G for the test set.

row= X_test.shape[0]

column= K_cent

G_test= numpy.empty((row,column), dtype= float)

for i in range(row):

	for j in range(column):

		dist= numpy.linalg.norm(X_test[i]-cent[j])

		G_test[i][j]= math.exp(-math.pow(dist,2)/math.pow(2*sigma,2))

step 11: Analyze the accuracy of prediction on test set

prediction= numpy.dot(G_test,W)

prediction= 0.5*(numpy.sign(prediction-0.5)+1)



score= accuracy_score(prediction,Y_test)

print score.mean()

With an RBF network, a prediction with an accuracy of 88% is achieved and so is the cause with MLP. However, the computational cost of training an MLP is much higher as compared to RBF; hence, here it's better to use RBF network instead of MLP.