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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