4. AI AND MACHINE LEARNING VTU LAB | READ NOW
MACHINE LEARNING VTU LAB – Backpropagation Algorithm
Program 4] BUILD AN ARTIFICIAL NEURAL NETWORK BY IMPLEMENTING THE BACKPROPAGATION ALGORITHM AND TEST THE SAME USING APPROPRIATE DATASETS.
Program Code – lab4.py
import numpy as np
X = np.array(([2, 9], [1, 5], [3, 6]), dtype=float) # X = (hours sleeping, hours studying)
y = np.array(([92], [86], [89]), dtype=float) # y = score on test
# scale units
X = X/np.amax(X, axis=0) # maximum of X array
y = y/100 # max test score is 100
class Neural_Network(object):
def __init__(self):
# Parameters
self.inputSize = 2
self.outputSize = 1
self.hiddenSize = 3
# Weights
self.W1 = np.random.randn(self.inputSize, self.hiddenSize) # (3x2) weight matrix from input to hidden layer
self.W2 = np.random.randn(self.hiddenSize, self.outputSize) # (3x1) weight matrix from hidden to output layer
def forward(self, X):
#forward propagation through our network
self.z = np.dot(X, self.W1) # dot product of X (input) and first set of 3x2 weights
self.z2 = self.sigmoid(self.z) # activation function
self.z3 = np.dot(self.z2, self.W2) # dot product of hidden layer (z2) and second set of 3x1 weights
o = self.sigmoid(self.z3) # final activation function
return o
def sigmoid(self, s):
return 1/(1+np.exp(-s)) # activation function
def sigmoidPrime(self, s):
return s * (1 - s) # derivative of sigmoid
def backward(self, X, y, o):
# backward propgate through the network
self.o_error = y - o # error in output
self.o_delta = self.o_error*self.sigmoidPrime(o) # applying derivative of sigmoid to
self.z2_error = self.o_delta.dot(self.W2.T) # z2 error: how much our hidden layer weights contributed to output error
self.z2_delta = self.z2_error*self.sigmoidPrime(self.z2) # applying derivative of sigmoid to z2 error
self.W1 += X.T.dot(self.z2_delta) # adjusting first set (input --> hidden) weights
self.W2 += self.z2.T.dot(self.o_delta) # adjusting second set (hidden --> output) weights
def train (self, X, y):
o = self.forward(X)
self.backward(X, y, o)
NN = Neural_Network()
print ("\nInput: \n" + str(X))
print ("\nActual Output: \n" + str(y))
print ("\nPredicted Output: \n" + str(NN.forward(X)))
print ("\nLoss: \n" + str(np.mean(np.square(y - NN.forward(X))))) # mean sum squared loss)
NN.train(X, y)
MACHINE LEARNING Program Execution – lab4.ipynb
Jupyter Notebook program execution.
import numpy as np X = np.array(([2, 9], [1, 5], [3, 6]), dtype=float) # X = (hours sleeping, hours studying) y = np.array(([92], [86], [89]), dtype=float) # y = score on test # scale units X = X/np.amax(X, axis=0) # maximum of X array y = y/100 # max test score is 100
class Neural_Network(object):
def __init__(self):
# Parameters
self.inputSize = 2
self.outputSize = 1
self.hiddenSize = 3
# Weights
self.W1 = np.random.randn(self.inputSize, self.hiddenSize) # (3x2) weight matrix from input to hidden layer
self.W2 = np.random.randn(self.hiddenSize, self.outputSize) # (3x1) weight matrix from hidden to output layer
def forward(self, X):
#forward propagation through our network
self.z = np.dot(X, self.W1) # dot product of X (input) and first set of 3x2 weights
self.z2 = self.sigmoid(self.z) # activation function
self.z3 = np.dot(self.z2, self.W2) # dot product of hidden layer (z2) and second set of 3x1 weights
o = self.sigmoid(self.z3) # final activation function
return o
def sigmoid(self, s):
return 1/(1+np.exp(-s)) # activation function
def sigmoidPrime(self, s):
return s * (1 - s) # derivative of sigmoid
def backward(self, X, y, o):
# backward propgate through the network
self.o_error = y - o # error in output
self.o_delta = self.o_error*self.sigmoidPrime(o) # applying derivative of sigmoid to
self.z2_error = self.o_delta.dot(self.W2.T) # z2 error: how much our hidden layer weights contributed to output error
self.z2_delta = self.z2_error*self.sigmoidPrime(self.z2) # applying derivative of sigmoid to z2 error
self.W1 += X.T.dot(self.z2_delta) # adjusting first set (input --> hidden) weights
self.W2 += self.z2.T.dot(self.o_delta) # adjusting second set (hidden --> output) weights
def train (self, X, y):
o = self.forward(X)
self.backward(X, y, o)
NN = Neural_Network()
for i in range(1000): # trains the NN 1,000 times
print ("\nInput: \n" + str(X))
print ("\nActual Output: \n" + str(y))
print ("\nPredicted Output: \n" + str(NN.forward(X)))
print ("\nLoss: \n" + str(np.mean(np.square(y - NN.forward(X))))) # mean sum squared loss)
NN.train(X, y)
Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.47212874] [0.42728946] [0.40891365]] Loss: 0.20642371917499927 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output:
show more (open the raw output data in a text editor) … Actual Output: [[0.92] [0.86] [0.89]]
Predicted Output: [[0.90664827] [0.85694302] [0.904511 ]] Loss: 0.00013272761631194843 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.90666572] [0.85696268] [0.90452085]] Loss:
show more (open the raw output data in a text editor) … [0.85762678] [0.90441548]] Loss: 0.00012413266964384637
Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.90739553] [0.85762866] [0.90441066]] Loss: 0.00012405438508618016 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output:
show more (open the raw output data in a text editor) …[[0.90801592] [0.85790991] [0.90332005]] Loss:
0.00010847015771193348 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.90801867] [0.85791115] [0.90331503]] Loss: 0.00010840182852314304 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]]
show more (open the raw output data in a text editor) … Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]]
Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.90843358] [0.85810301] [0.90255937]] Loss: 9.837281731803699e-05 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output:
show more (open the raw output data in a text editor) …8.405495434787463e-05 Input: [[0.66666667 1. ] [0.33333333 0.55555556]
[1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]] Predicted Output: [[0.90907296] [0.85841616] [0.90140598]] Loss: 8.400178305772788e-05 Input: [[0.66666667 1. ] [0.33333333 0.55555556] [1. 0.66666667]] Actual Output: [[0.92] [0.86] [0.89]]
show more (open the raw output data in a text editor) … [0.85857961] [0.90083551]] Loss: 7.731308968994962e-05
