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bpnn solve kindergarten problem
# Back-Propagation Neural Networks
# another way: solve it as a Regression Problem
# Written in Python. See http://www.python.org/
# Modified by JSun to solve the problem here: http://www.weibo.com/1497035431/ynPEvC78V
# 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
def argmax(L):
idx_max = -1
v_max = 0
for i,x in enumerate(L):
if idx_max == -1:
v_max = x
idx_max = i
if x>v_max:
idx_max = i
v_max =x
return idx_max
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)
self.ao[k] = 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
output_deltas[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):
result = []
for p in patterns:
ttt = self.update(p[0])
result.append(round(ttt[0]))
return result
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=3000, N=0.01, M=0.001):
# 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
print n.test(pat)
def R(n):
return [n]
def Q(L):
H = [0]*10
for x in L:
H[x]+=1
return H
def demo_digit():
pat = [
[Q([7,1,1,1]), R(0)],
[Q([8,8,0,9]), R(6)],
[Q([2,1,7,2]), R(0)],
[Q([6,6,6,6]), R(4)],
[Q([1,1,1,1]), R(0)],
[Q([2,2,2,2]), R(0)],
[Q([7,6,6,2]), R(2)],
[Q([9,3,1,3]), R(1)],
[Q([0,0,0,0]), R(4)],
[Q([5,5,5,5]), R(0)],
[Q([8,1,9,3]), R(3)],
[Q([8,0,9,6]), R(5)],
[Q([4,3,9,8]), R(3)],
[Q([9,4,7,5]), R(1)],
[Q([9,0,3,8]), R(4)],
[Q([3,1,4,8]), R(2)]
]
# create a network with two input, two hidden, and one output nodes
n = NN(10, 10, 1)
# train it with some patterns
n.train(pat)
# test it
#tt = [ [Q([2,8,8,9]),[0]*10] ]
tt = pat
print n.test(tt)
tt = [ [Q([2,8,8,9]),[0]] ]
print n.test(tt)
if __name__ == '__main__':
demo_digit()
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