nn.py

"""
Pure Python implementation of a Back-Propagation Neural Network using the
hyperbolic tangent as the sigmoid squashing function.

Original Author: Neil Schemenauer <nas@arctrix.com>
Modified Author: James Howard <james.w.howard@gmail.com>

Modified to work for function regression and added option to use matplotlib
to display regression networks.

Code is placed in public domain.
"""

import math
import random

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 plot(inputs, outputs, actual):
    """Plot a given function.  
    
    The actual function will be plotted with a line and the outputs with 
    points.  Useful for visualizing the error of the neural networks attempt 
    at function interpolation."""
    try:
        import matplotlib.pyplot
    except:
        raise ImportError, "matplotlib package not found."
    fig = matplotlib.pyplot.figure()
    ax1 = fig.add_subplot(111)
    ax1.plot(inputs, actual, 'b-')
    ax1.plot(inputs, outputs, 'r.')
    matplotlib.pyplot.draw()
    
    

class NN:
    def __init__(self, ni, nh, no, regression = False):
        """NN constructor.
        
        ni, nh, no are the number of input, hidden and output nodes.
        regression is used to determine if the Neural network will be trained 
        and used as a classifier or for function regression.
        """
        
        self.regression = regression
        
        #Number of input, hidden and output nodes.
        self.ni = ni  + 1 # +1 for bias node
        self.nh = nh  + 1 # +1 for bias node
        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(-1, 1)
        for j in range(self.nh):
            for k in range(self.no):
                self.wo[j][k] = rand(-1, 1)

        # 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] = inputs[i]

        # hidden activations
        for j in range(self.nh - 1):
            total = 0.0
            for i in range(self.ni):
                total += self.ai[i] * self.wi[i][j]
            self.ah[j] = sigmoid(total)

        # output activations
        for k in range(self.no):
            total = 0.0
            for j in range(self.nh):
                total += self.ah[j] * self.wo[j][k]
            self.ao[k] = total
            if not self.regression:
                self.ao[k] = sigmoid(total)
            
        
        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):
            output_deltas[k] = targets[k] - self.ao[k]
            if not self.regression:
                output_deltas[k] = dsigmoid(self.ao[k]) * output_deltas[k]

        
        # 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 += 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

        # 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 += 0.5*((targets[k]-self.ao[k])**2)
        return error


    def test(self, patterns, verbose = False):
        tmp = []
        for p in patterns:
            if verbose:
                print p[0], '->', self.update(p[0])
            tmp.append(self.update(p[0]))

        return tmp

        
    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, verbose = False):
        """Train the neural network.  
        
        N is the learning rate.
        M is the momentum factor.
        """
        for i in xrange(iterations):
            error = 0.0
            for p in patterns:
                self.update(p[0])
                tmp = self.backPropagate(p[1], N, M)
                error += tmp
                
            if i % 100 == 0:
                print 'error %-14f' % error
            

def demoRegression():
    data = []
    inputs = []
    actual = []

    domain = [-1, 1]
    steps = 50
    stepsize = (domain[1] - domain[0]) / ((steps - 1)*1.0)

    #Teach the network the function y = x**2
    for i in range(steps):
        x = domain[0] + stepsize * i
        y = x**2
        
        data.append([[x], [y]])
        inputs.append(x)
        actual.append(y)
        
    n = NN(1, 4, 1, regression = True)
    
    #Train and test the nural network.
    n.train(data, 1000, 0.2, 0.1, False)
    outputs = n.test(data, verbose = True)
    
    #Plot the function.
    try:
        plot(inputs, outputs, actual)
        print "Press a key to quit."
        value = raw_input()
    except:
        print "Must have matplotlib to plot."


def demoClassification():
    # 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, regression = False)

    # train it with some patterns then test it.
    n.train(pat, 1000, 0.5, 0.2)
    n.test(pat, verbose = True)


if __name__ == '__main__':
    #demoRegression()
    demoClassification()