#!/usr/bin/python # Back-Propagation Neural Networks # # Written in Python. See https://www.python.org/ # # Neil Schemenauer <nascheme@enme.ucalgary.ca> import math import random as random # Local imports import util random.seed(0) # calculate a random number where: a <= rand < b def rand(a, b, random=random.random): return (b-a)*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 class NN(object): # print '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 values for i in range(self.ni): for j in range(self.nh): self.wi[i][j] = rand(-2.0, 2.0) 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): # print 'update', 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] = 1.0/(1.0+math.exp(-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] = 1.0/(1.0+math.exp(-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] = 1.0/(1.0+math.exp(-sum)) return self.ao[:] def backPropagate(self, targets, N, M): # print 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 # print self.no for k in range(self.no): ao = self.ao[k] output_deltas[k] = ao*(1-ao)*(targets[k]-ao) # calculate error terms for hidden hidden_deltas = [0.0] * self.nh for j in range(self.nh): sum = 0.0 for k in range(self.no): sum = sum + output_deltas[k]*self.wo[j][k] hidden_deltas[j] = self.ah[j]*(1-self.ah[j])*sum # 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 # 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('%s -> %s' % (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=2000, 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 i, 'error %-14f' % 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 two output nodes n = NN(2, 3, 1) # train it with some patterns n.train(pat, 5000) # test it #n.test(pat) def time(fn, *args): import time, traceback begin = time.time() result = fn(*args) end = time.time() return result, end-begin def test_bpnn(iterations): times = [] for _ in range(iterations): result, t = time(demo) times.append(t) return times main = test_bpnn if __name__ == "__main__": import optparse parser = optparse.OptionParser( usage="%prog [options]", description=("Test the performance of a neural network.")) util.add_standard_options_to(parser) options, args = parser.parse_args() util.run_benchmark(options, options.num_runs, test_bpnn)