python ocr(光学文字识别)学习笔记 （二）

"""
In order to decide how many hidden nodes the hidden layer should have,
split up the data set into training and testing data and create networks
with various hidden node counts (5, 10, 15, ... 45), testing the performance
for each.

The best-performing node count is used in the actual system. If multiple counts
perform similarly, choose the smallest count for a smaller network with fewer computations.
"""

import numpy as np
from ocr import OCRNeuralNetwork
from sklearn.cross_validation import train_test_split

def test(data_matrix, data_labels, test_indices, nn):
    avg_sum = 0
    for j in xrange(100):
        correct_guess_count = 0
        for i in test_indices:
            test = data_matrix[i]
            prediction = nn.predict(test)
            if data_labels[i] == prediction:
                correct_guess_count += 1

        avg_sum += (correct_guess_count / float(len(test_indices)))
    return avg_sum / 100


# Load data samples and labels into matrix
data_matrix = np.loadtxt(open(‘data.csv‘, ‘rb‘), delimiter = ‘,‘).tolist()
data_labels = np.loadtxt(open(‘dataLabels.csv‘, ‘rb‘)).tolist()

# Create training and testing sets.
train_indices, test_indices = train_test_split(list(range(5000)))

print "PERFORMANCE"
print "-----------"

# Try various number of hidden nodes and see what performs best
for i in xrange(5, 50, 5):
    nn = OCRNeuralNetwork(i, data_matrix, data_labels, train_indices, False)
    performance = str(test(data_matrix, data_labels, test_indices, nn))
    print "{i} Hidden Nodes: {val}".format(i=i, val=performance)

import csv
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
from numpy import matrix
from math import pow
from collections import namedtuple
import math
import random
import os
import json

"""
This class does some initial training of a neural network for predicting drawn
digits based on a data set in data_matrix and data_labels. It can then be used to
train the network further by calling train() with any array of data or to predict
what a drawn digit is by calling predict().

The weights that define the neural network can be saved to a file, NN_FILE_PATH,
to be reloaded upon initilization.
"""
class OCRNeuralNetwork:
    LEARNING_RATE = 0.1
    WIDTH_IN_PIXELS = 20
    NN_FILE_PATH = ‘nn.json‘

    def __init__(self, num_hidden_nodes, data_matrix, data_labels, training_indices, use_file=True):
        self.sigmoid = np.vectorize(self._sigmoid_scalar)
        self.sigmoid_prime = np.vectorize(self._sigmoid_prime_scalar)
        self._use_file = use_file
        self.data_matrix = data_matrix
        self.data_labels = data_labels

        if (not os.path.isfile(OCRNeuralNetwork.NN_FILE_PATH) or not use_file):
            # Step 1: Initialize weights to small numbers
            self.theta1 = self._rand_initialize_weights(400, num_hidden_nodes)
            self.theta2 = self._rand_initialize_weights(num_hidden_nodes, 10)
            self.input_layer_bias = self._rand_initialize_weights(1, num_hidden_nodes)
            self.hidden_layer_bias = self._rand_initialize_weights(1, 10)

            # Train using sample data
            TrainData = namedtuple(‘TrainData‘, [‘y0‘, ‘label‘])
            self.train([TrainData(self.data_matrix[i], int(self.data_labels[i])) for i in training_indices])
            self.save()
        else:
            self._load()

    def _rand_initialize_weights(self, size_in, size_out):
        return [((x * 0.12) - 0.06) for x in np.random.rand(size_out, size_in)]

    # The sigmoid activation function. Operates on scalars.
    def _sigmoid_scalar(self, z):
        return 1 / (1 + math.e ** -z)

    def _sigmoid_prime_scalar(self, z):
        return self.sigmoid(z) * (1 - self.sigmoid(z))

    def _draw(self, sample):
        pixelArray = [sample[j:j+self.WIDTH_IN_PIXELS] for j in xrange(0, len(sample), self.WIDTH_IN_PIXELS)]
        plt.imshow(zip(*pixelArray), cmap = cm.Greys_r, interpolation="nearest")
        plt.show()

    def train(self, training_data_array):
        for data in training_data_array:
            # Step 2: Forward propagation
            y1 = np.dot(np.mat(self.theta1), np.mat(data[‘y0‘]).T)
            sum1 =  y1 + np.mat(self.input_layer_bias) # Add the bias
            y1 = self.sigmoid(sum1)

            y2 = np.dot(np.array(self.theta2), y1)
            y2 = np.add(y2, self.hidden_layer_bias) # Add the bias
            y2 = self.sigmoid(y2)

            # Step 3: Back propagation
            actual_vals = [0] * 10 # actual_vals is a python list for easy initialization and is later turned into an np matrix (2 lines down).
            actual_vals[data[‘label‘]] = 1
            output_errors = np.mat(actual_vals).T - np.mat(y2)
            hidden_errors = np.multiply(np.dot(np.mat(self.theta2).T, output_errors), self.sigmoid_prime(sum1))

            # Step 4: Update weights
            self.theta1 += self.LEARNING_RATE * np.dot(np.mat(hidden_errors), np.mat(data[‘y0‘]))
            self.theta2 += self.LEARNING_RATE * np.dot(np.mat(output_errors), np.mat(y1).T)
            self.hidden_layer_bias += self.LEARNING_RATE * output_errors
            self.input_layer_bias += self.LEARNING_RATE * hidden_errors

    def predict(self, test):
        y1 = np.dot(np.mat(self.theta1), np.mat(test).T)
        y1 =  y1 + np.mat(self.input_layer_bias) # Add the bias
        y1 = self.sigmoid(y1)

        y2 = np.dot(np.array(self.theta2), y1)
        y2 = np.add(y2, self.hidden_layer_bias) # Add the bias
        y2 = self.sigmoid(y2)

        results = y2.T.tolist()[0]
        return results.index(max(results))

    def save(self):
        if not self._use_file:
            return

        json_neural_network = {
            "theta1":[np_mat.tolist()[0] for np_mat in self.theta1],
            "theta2":[np_mat.tolist()[0] for np_mat in self.theta2],
            "b1":self.input_layer_bias[0].tolist()[0],
            "b2":self.hidden_layer_bias[0].tolist()[0]
        };
        with open(OCRNeuralNetwork.NN_FILE_PATH,‘w‘) as nnFile:
            json.dump(json_neural_network, nnFile)

    def _load(self):
        if not self._use_file:
            return

        with open(OCRNeuralNetwork.NN_FILE_PATH) as nnFile:
            nn = json.load(nnFile)
        self.theta1 = [np.array(li) for li in nn[‘theta1‘]]
        self.theta2 = [np.array(li) for li in nn[‘theta2‘]]
        self.input_layer_bias = [np.array(nn[‘b1‘][0])]
        self.hidden_layer_bias = [np.array(nn[‘b2‘][0])]