# Back-Propagation Neural Networks
#
# Written in Python. See http://www.python.org/
# Placed in the public domain.
# Neil Schemenauer <nas@arctrix.com>
import math
import random
import string
random.seed(0)
# calculate a random number where: a <= rand < b
def rand(a, b):
return (b-a)*random.random() + a
# Make a matrix (we could use NumPy to speed this up)
def makeMatrix(I, J, fill=0.0):
m = []
for i in range(I):
m.append([fill]*J)
return m
# our sigmoid function, tanh is a little nicer than the standard 1/(1+e^-x)
def sigmoid(x):
return math.tanh(x)
# derivative of our sigmoid function, in terms of the output (i.e. y)
def dsigmoid(y):
return 1.0 - y**2
class NN:
def __init__(self, ni, nh, no):
# number of input, hidden, and output nodes
self.ni = ni + 1 # +1 for bias node
self.nh = nh
self.no = no
# activations for nodes
self.ai = [1.0]*self.ni
self.ah = [1.0]*self.nh
self.ao = [1.0]*self.no
# create weights
self.wi = makeMatrix(self.ni, self.nh)
self.wo = makeMatrix(self.nh, self.no)
# set them to random vaules
for i in range(self.ni):
for j in range(self.nh):
self.wi[i][j] = rand(-0.2, 0.2)
for j in range(self.nh):
for k in range(self.no):
self.wo[j][k] = rand(-2.0, 2.0)
# last change in weights for momentum
self.ci = makeMatrix(self.ni, self.nh)
self.co = makeMatrix(self.nh, self.no)
def update(self, inputs):
if len(inputs) != self.ni-1:
raise ValueError(‘wrong number of inputs‘)
# input activations
for i in range(self.ni-1):
#self.ai[i] = sigmoid(inputs[i])
self.ai[i] = inputs[i]
# hidden activations
for j in range(self.nh):
sum = 0.0
for i in range(self.ni):
sum = sum + self.ai[i] * self.wi[i][j]
self.ah[j] = sigmoid(sum)
# output activations
for k in range(self.no):
sum = 0.0
for j in range(self.nh):
sum = sum + self.ah[j] * self.wo[j][k]
self.ao[k] = sigmoid(sum)
return self.ao[:]
def backPropagate(self, targets, N, M):
if len(targets) != self.no:
raise ValueError(‘wrong number of target values‘)
# calculate error terms for output
output_deltas = [0.0] * self.no
for k in range(self.no):
error = targets[k]-self.ao[k]
output_deltas[k] = dsigmoid(self.ao[k]) * error
# calculate error terms for hidden
hidden_deltas = [0.0] * self.nh
for j in range(self.nh):
error = 0.0
for k in range(self.no):
error = error + output_deltas[k]*self.wo[j][k]
hidden_deltas[j] = dsigmoid(self.ah[j]) * error
# update output weights
for j in range(self.nh):
for k in range(self.no):
change = output_deltas[k]*self.ah[j]
self.wo[j][k] = self.wo[j][k] + N*change + M*self.co[j][k]
self.co[j][k] = change
#print N*change, M*self.co[j][k]
# update input weights
for i in range(self.ni):
for j in range(self.nh):
change = hidden_deltas[j]*self.ai[i]
self.wi[i][j] = self.wi[i][j] + N*change + M*self.ci[i][j]
self.ci[i][j] = change
# calculate error
error = 0.0
for k in range(len(targets)):
error = error + 0.5*(targets[k]-self.ao[k])**2
return error
def test(self, patterns):
for p in patterns:
print(p[0], ‘->‘, self.update(p[0]))
def weights(self):
print(‘Input weights:‘)
for i in range(self.ni):
print(self.wi[i])
print()
print(‘Output weights:‘)
for j in range(self.nh):
print(self.wo[j])
def train(self, patterns, iterations=1000, N=0.5, M=0.1):
# N: learning rate
# M: momentum factor
for i in range(iterations):
error = 0.0
for p in patterns:
inputs = p[0]
targets = p[1]
self.update(inputs)
error = error + self.backPropagate(targets, N, M)
if i % 100 == 0:
print(‘error %-.5f‘ % error)
def demo():
# Teach network XOR function
pat = [
[[0,0], [0]],
[[0,1], [1]],
[[1,0], [1]],
[[1,1], [0]]
]
# create a network with two input, two hidden, and one output nodes
n = NN(2, 2, 1)
# train it with some patterns
n.train(pat)
# test it
n.test(pat)
if __name__ == ‘__main__‘:
demo()