1. Use Keras Model with three layers of neural network to classify the dataset in HW#2 (for both questions). The first layer (input layer) has four neurons, the second layer has three neurons, and the third layer (output layer) has only one neuron. You should use at least two different activation function and two different optimization functions.

Explain your experience with this network in compare with the ones you did in HW#2 and also the effect of different activation and optimization functions.

Hint: Go over the following video

https://www.youtube.com/watch?v=bemDFpNooA8&ab_channel=TensorFlow

***********HW#2*************

HW#2 question 1 code :

import numpy as np

import random

# In[116]:

xin=[[0,0,1],

[0,1,1],

[1,0,1],

[1,1,1]]

t= [1, 1, 1, 0]

for i in range(0,4):

print(xin[i][0], xin[i][1])

print(t)

# In[117]:

w1 = [[random.uniform(-2.0,2) for i in range(13)] ]

print(w1[0][11])

print(w1)

# In[118]:

w2 = [[random.uniform(-2.0,2) for i in range(4)] ]

print(w2)

print(w2[0][2])

lr= 0.1

# In[119]:

def sigmoid(x):

return (1/(1+np.exp(-x)))

# In[120]:

while True:

total_error = 0

for i in range(0,4):

v1= (xin[i][0]*w1[0][0] + xin[i][1]*w1[0][1] + w1[0][2])

v2= (xin[i][0]*w1[0][3] + xin[i][1]*w1[0][4] + w1[0][5])

v3= (xin[i][0]*w1[0][6] + xin[i][1]*w1[0][7] + w1[0][8])

v4 = (xin[i][0]*w1[0][9] + xin[i][1]*w1[0][10] + w1[0][11])

y1=sigmoid(v1)

y2=sigmoid(v2)

y3=sigmoid(v3)

y4=sigmoid(v4)

#print(y1,y2,y3)

u = y1 * w1[0][12] + y2 * w2[0][0] + y3 * w2[0][1] + y4 * w2[0][2] + w2[0][3]

y = sigmoid(u)

print(y)

error = np.square(t[i]- y)

d_error = (t[i]-y)

dw112 = lr * d_error * y * (1-y) * y1

dw20 = lr * d_error * y * (1-y) * y2

dw21 = lr * d_error * y * (1-y) * y3

dw22 = lr * d_error * y * (1-y) * y4

dw23 = lr * d_error * y * (1-y)

w1[0][12] = w1[0][12] + dw112

w2[0][0] = w2[0][0] + dw20

w2[0][1] = w2[0][1] + dw21

w2[0][2] = w2[0][2] + dw22

w2[0][3] = w2[0][3] + dw23

sum = w1[0][12]*y*(1-y)*d_error + w2[0][0]*y*(1-y)*d_error + w2[0][1]*y*(1-y)*d_error + w2[0][2]*y*(1-y)*d_error

dw1 = y1 * (1-y1) * xin[i][0] * sum

dw2 = y1 * (1-y1) * xin[i][1] * sum

dw3 = y1 * (1-y1) * sum

dw4 = y2 * (1-y2) * xin[i][0] * sum

dw5 = y2 * (1-y2) * xin[i][1] * sum

dw6 = y2 * (1-y2) * sum

dw7 = y3 * (1-y3) * xin[i][0] * sum

dw8 = y3 * (1-y3) * xin[i][1] * sum

dw9 = y3 * (1-y3) * sum

dw10 = y4 * (1-y4) * xin[i][0] * sum

dw11 = y4 * (1-y4) * xin[i][1] * sum

dw12 = y4 * (1-y4) * sum

w1[0][0] = w1[0][1] +dw1

w1[0][1] = w1[0][1] +dw2

w1[0][2] = w1[0][2] +dw3

w1[0][3] = w1[0][3] +dw4

w1[0][4] = w1[0][4] +dw5

w1[0][5] = w1[0][5] +dw6

w1[0][6] = w1[0][6] +dw7

w1[0][7] = w1[0][7] +dw8

w1[0][8] = w1[0][8] +dw9

w1[0][9] = w1[0][9] + dw10

w1[0][10] = w1[0][10] + dw11

w1[0][11] = w1[0][11] + dw12

total_error = total_error + error

#print(total_error)

if (total_error<0.01):

print("The Last 4 will be the Output")

break

print(" First layer weights: ")

for i in range(0,13):

print(w1[0][i])

print(" Second layer weights: ")

for i in range(0,4):

print(w2[0][i])

print(" The target outputs are: ")

print(t)

HW#2 question 2 code :

import numpy as np

import random

# In[59]:

x1 = np.random.uniform(0,3,size=(50,2))

x2 = np.random.uniform(6,9,size=(50,2))

t = [0 for i in range(50)]

t += [1 for i in range(50)]

x = np.append(x1,x2,axis=0)

print(x)

# In[60]:

w1 = [[random.uniform(-2.0,2) for i in range(13)]]

w2 = [[random.uniform(-2.0,2) for i in range(4)]]

lr = 0.1

print(w1)

# In[61]:

def sigmoid(x):

y = 1/(1 + np.exp(-x))

return y

# In[62]:

while True:

total_error = 0

output = []

for i in range(0,100):

v1= (x[i][0]*w1[0][0] + x[i][1]*w1[0][1] + w1[0][2])

v2= (x[i][0]*w1[0][3] + x[i][1]*w1[0][4] + w1[0][5])

v3= (x[i][0]*w1[0][6] + x[i][1]*w1[0][7] + w1[0][8])

v4 = (x[i][0]*w1[0][9] + x[i][1]*w1[0][10] + w1[0][11])

y1=sigmoid(v1)

y2=sigmoid(v2)

y3=sigmoid(v3)

y4=sigmoid(v4)

u = y1 * w1[0][12] + y2 * w2[0][0] + y3 * w2[0][1] + y4 * w2[0][2] + w2[0][3]

y = sigmoid(u)

print(y)

output.insert(i,y)

error = np.square(t[i]- y)

d_error = (t[i]-y)

dw112 = lr * d_error * y * (1-y) * y1

dw20 = lr * d_error * y * (1-y) * y2

dw21 = lr * d_error * y * (1-y) * y3

dw22 = lr * d_error * y * (1-y) * y4

dw23 = lr * d_error * y * (1-y)

w1[0][12] = w1[0][12] + dw112

w2[0][0] = w2[0][0] + dw20

w2[0][1] = w2[0][1] + dw21

w2[0][2] = w2[0][2] + dw22

w2[0][3] = w2[0][3] + dw23

sum = w1[0][12]*y*(1-y)*d_error + w2[0][0]*y*(1-y)*d_error + w2[0][1]*y*(1-y)*d_error + w2[0][2]*y*(1-y)*d_error

dw1 = y1 * (1-y1) * x[i][0] * sum

dw2 = y1 * (1-y1) * x[i][1] * sum

dw3 = y1 * (1-y1) * sum

dw4 = y2 * (1-y2) * x[i][0] * sum

dw5 = y2 * (1-y2) * x[i][1] * sum

dw6 = y2 * (1-y2) * sum

dw7 = y3 * (1-y3) * x[i][0] * sum

dw8 = y3 * (1-y3) * x[i][1] * sum

dw9 = y3 * (1-y3) * sum

dw10 = y4 * (1-y4) * x[i][0] * sum

dw11 = y4 * (1-y4) * x[i][1] * sum

dw12 = y4 * (1-y4) * sum

w1[0][0] = w1[0][1] +dw1

w1[0][1] = w1[0][1] +dw2

w1[0][2] = w1[0][2] +dw3

w1[0][3] = w1[0][3] +dw4

w1[0][4] = w1[0][4] +dw5

w1[0][5] = w1[0][5] +dw6

w1[0][6] = w1[0][6] +dw7

w1[0][7] = w1[0][7] +dw8

w1[0][8] = w1[0][8] +dw9

w1[0][9] = w1[0][9] + dw10

w1[0][10] = w1[0][10] + dw11

w1[0][11] = w1[0][11] + dw12

total_error = total_error + error

#print(total_error)

if (total_error < 0.01):

print(" The Output ")

break

print (" Target output: ", t)

print (" Predicted Output y: ", output)

print(" First layer weights: ")

for i in range(0,13):

print(w1[0][i])

print(" Second layer weights: ")

for i in range(0,4):

print(w2[0][i])