source code for article 1 to 7

activators.py

@@ -0,0 +1,38 @@
+#!/usr/bin/env python
+# -*- coding: UTF-8 -*-
+
+
+import numpy as np
+
+
+class ReluActivator(object):
+    def forward(self, weighted_input):
+        #return weighted_input
+        return max(0, weighted_input)
+
+    def backward(self, output):
+        return 1 if output > 0 else 0
+
+
+class IdentityActivator(object):
+    def forward(self, weighted_input):
+        return weighted_input
+
+    def backward(self, output):
+        return 1
+
+
+class SigmoidActivator(object):
+    def forward(self, weighted_input):
+        return 1.0 / (1.0 + np.exp(-weighted_input))
+
+    def backward(self, output):
+        return output * (1 - output)
+
+
+class TanhActivator(object):
+    def forward(self, weighted_input):
+        return 2.0 / (1.0 + np.exp(-2 * weighted_input)) - 1.0
+
+    def backward(self, output):
+        return 1 - output * output

bp.py

@@ -0,0 +1,303 @@
+#!/usr/bin/env python
+# -*- coding: UTF-8 -*-
+
+
+import random
+from numpy import *
+
+
+def sigmoid(inX):
+    return 1.0 / (1 + exp(-inX))
+
+
+class Node(object):
+    def __init__(self, layer_index, node_index):
+        self.layer_index = layer_index
+        self.node_index = node_index
+        self.downstream = []
+        self.upstream = []
+        self.output = 0
+        self.delta = 0
+
+    def set_output(self, output):
+        self.output = output
+
+    def append_downstream_connection(self, conn):
+        self.downstream.append(conn)
+
+    def append_upstream_connection(self, conn):
+        self.upstream.append(conn)
+
+    def calc_output(self):
+        output = reduce(lambda ret, conn: ret + conn.upstream_node.output * conn.weight, self.upstream, 0)
+        self.output = sigmoid(output)
+
+    def calc_hidden_layer_delta(self):
+        downstream_delta = reduce(
+            lambda ret, conn: ret + conn.downstream_node.delta * conn.weight,
+            self.downstream, 0.0)
+        self.delta = self.output * (1 - self.output) * downstream_delta
+
+    def calc_output_layer_delta(self, label):
+        self.delta = self.output * (1 - self.output) * (label - self.output)
+
+    def __str__(self):
+        node_str = '%u-%u: output: %f delta: %f' % (self.layer_index, self.node_index, self.output, self.delta)
+        downstream_str = reduce(lambda ret, conn: ret + '\n\t' + str(conn), self.downstream, '')
+        upstream_str = reduce(lambda ret, conn: ret + '\n\t' + str(conn), self.upstream, '')
+        return node_str + '\n\tdownstream:' + downstream_str + '\n\tupstream:' + upstream_str 
+
+
+class ConstNode(object):
+    def __init__(self, layer_index, node_index):
+        self.layer_index = layer_index
+        self.node_index = node_index
+        self.downstream = []
+        self.output = 1
+
+    def append_downstream_connection(self, conn):
+        self.downstream.append(conn)
+
+    def calc_hidden_layer_delta(self):
+        downstream_delta = reduce(
+            lambda ret, conn: ret + conn.downstream_node.delta * conn.weight,
+            self.downstream, 0.0)
+        self.delta = self.output * (1 - self.output) * downstream_delta
+
+    def __str__(self):
+        node_str = '%u-%u: output: 1' % (self.layer_index, self.node_index)
+        downstream_str = reduce(lambda ret, conn: ret + '\n\t' + str(conn), self.downstream, '')
+        return node_str + '\n\tdownstream:' + downstream_str
+
+
+class Layer(object):
+    def __init__(self, layer_index, node_count):
+        self.layer_index = layer_index
+        self.nodes = []
+        for i in range(node_count):
+            self.nodes.append(Node(layer_index, i))
+        self.nodes.append(ConstNode(layer_index, node_count))
+
+    def set_output(self, data):
+        for i in range(len(data)):
+            self.nodes[i].set_output(data[i])
+
+    def calc_output(self):
+        for node in self.nodes[:-1]:
+            node.calc_output()
+
+    def dump(self):
+        for node in self.nodes:
+            print node
+
+
+class Connection(object):
+    def __init__(self, upstream_node, downstream_node):
+        self.upstream_node = upstream_node
+        self.downstream_node = downstream_node
+        self.weight = random.uniform(-0.1, 0.1)
+        self.gradient = 0.0
+
+    def calc_gradient(self):
+        self.gradient = self.downstream_node.delta * self.upstream_node.output
+
+    def update_weight(self, rate):
+        self.calc_gradient()
+        self.weight += rate * self.gradient
+
+    def get_gradient(self):
+        return self.gradient
+
+    def __str__(self):
+        return '(%u-%u) -> (%u-%u) = %f' % (
+            self.upstream_node.layer_index, 
+            self.upstream_node.node_index,
+            self.downstream_node.layer_index, 
+            self.downstream_node.node_index, 
+            self.weight)
+
+
+class Connections(object):
+    def __init__(self):
+        self.connections = []
+
+    def add_connection(self, connection):
+        self.connections.append(connection)
+
+    def dump(self):
+        for conn in self.connections:
+            print conn
+
+
+class Network(object):
+    def __init__(self, layers):
+        self.connections = Connections()
+        self.layers = []
+        layer_count = len(layers)
+        node_count = 0;
+        for i in range(layer_count):
+            self.layers.append(Layer(i, layers[i]))
+        for layer in range(layer_count - 1):
+            connections = [Connection(upstream_node, downstream_node) 
+                           for upstream_node in self.layers[layer].nodes
+                           for downstream_node in self.layers[layer + 1].nodes[:-1]]
+            for conn in connections:
+                self.connections.add_connection(conn)
+                conn.downstream_node.append_upstream_connection(conn)
+                conn.upstream_node.append_downstream_connection(conn)
+
+
+    def train(self, labels, data_set, rate, epoch):
+        for i in range(epoch):
+            for d in range(len(data_set)):
+                self.train_one_sample(labels[d], data_set[d], rate)
+                # print 'sample %d training finished' % d
+
+    def train_one_sample(self, label, sample, rate):
+        self.predict(sample)
+        self.calc_delta(label)
+        self.update_weight(rate)
+
+    def calc_delta(self, label):
+        output_nodes = self.layers[-1].nodes
+        for i in range(len(label)):
+            output_nodes[i].calc_output_layer_delta(label[i])
+        for layer in self.layers[-2::-1]:
+            for node in layer.nodes:
+                node.calc_hidden_layer_delta()
+
+    def update_weight(self, rate):
+        for layer in self.layers[:-1]:
+            for node in layer.nodes:
+                for conn in node.downstream:
+                    conn.update_weight(rate)
+
+    def calc_gradient(self):
+        for layer in self.layers[:-1]:
+            for node in layer.nodes:
+                for conn in node.downstream:
+                    conn.calc_gradient()
+
+    def get_gradient(self, label, sample):
+        self.predict(sample)
+        self.calc_delta(label)
+        self.calc_gradient()
+
+    def predict(self, sample):
+        self.layers[0].set_output(sample)
+        for i in range(1, len(self.layers)):
+            self.layers[i].calc_output()
+        return map(lambda node: node.output, self.layers[-1].nodes[:-1])
+
+    def dump(self):
+        for layer in self.layers:
+            layer.dump()
+
+
+class Normalizer(object):
+    def __init__(self):
+        self.mask = [
+            0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80
+        ]
+
+    def norm(self, number):
+        return map(lambda m: 0.9 if number & m else 0.1, self.mask)
+
+    def denorm(self, vec):
+        binary = map(lambda i: 1 if i > 0.5 else 0, vec)
+        for i in range(len(self.mask)):
+            binary[i] = binary[i] * self.mask[i]
+        return reduce(lambda x,y: x + y, binary)
+
+
+def mean_square_error(vec1, vec2):
+    return 0.5 * reduce(lambda a, b: a + b, 
+                        map(lambda v: (v[0] - v[1]) * (v[0] - v[1]),
+                            zip(vec1, vec2)
+                        )
+                 )
+
+
+def gradient_check(network, sample_feature, sample_label):
+    '''
+    梯度检查
+    network: 神经网络对象
+    sample_feature: 样本的特征
+    sample_label: 样本的标签
+    '''
+    # 计算网络误差
+    network_error = lambda vec1, vec2: \
+            0.5 * reduce(lambda a, b: a + b, 
+                      map(lambda v: (v[0] - v[1]) * (v[0] - v[1]),
+                          zip(vec1, vec2)))
+
+    # 获取网络在当前样本下每个连接的梯度
+    network.get_gradient(sample_feature, sample_label)
+
+    # 对每个权重做梯度检查    
+    for conn in network.connections.connections: 
+        # 获取指定连接的梯度
+        actual_gradient = conn.get_gradient()
+
+        # 增加一个很小的值，计算网络的误差
+        epsilon = 0.0001
+        conn.weight += epsilon
+        error1 = network_error(network.predict(sample_feature), sample_label)
+
+        # 减去一个很小的值，计算网络的误差
+        conn.weight -= 2 * epsilon # 刚才加过了一次，因此这里需要减去2倍
+        error2 = network_error(network.predict(sample_feature), sample_label)
+
+        # 根据式6计算期望的梯度值
+        expected_gradient = (error2 - error1) / (2 * epsilon)
+
+        # 打印
+        print 'expected gradient: \t%f\nactual gradient: \t%f' % (
+            expected_gradient, actual_gradient)
+
+
+def train_data_set():
+    normalizer = Normalizer()
+    data_set = []
+    labels = []
+    for i in range(0, 256, 8):
+        n = normalizer.norm(int(random.uniform(0, 256)))
+        data_set.append(n)
+        labels.append(n)
+    return labels, data_set
+
+
+def train(network):
+    labels, data_set = train_data_set()
+    network.train(labels, data_set, 0.3, 50)
+
+
+def test(network, data):
+    normalizer = Normalizer()
+    norm_data = normalizer.norm(data)
+    predict_data = network.predict(norm_data)
+    print '\ttestdata(%u)\tpredict(%u)' % (
+        data, normalizer.denorm(predict_data))
+
+
+def correct_ratio(network):
+    normalizer = Normalizer()
+    correct = 0.0;
+    for i in range(256):
+        if normalizer.denorm(network.predict(normalizer.norm(i))) == i:
+            correct += 1.0
+    print 'correct_ratio: %.2f%%' % (correct / 256 * 100)
+
+
+def gradient_check_test():
+    net = Network([2, 2, 2])
+    sample_feature = [0.9, 0.1]
+    sample_label = [0.9, 0.1]
+    gradient_check(net, sample_feature, sample_label)
+
+
+if __name__ == '__main__':
+    net = Network([8, 3, 8])
+    train(net)
+    net.dump()
+    correct_ratio(net)