bp.py

#!/usr/bin/env python
# -*- coding: UTF-8 -*-

import random
from numpy import *
from functools import reduce
# 全连接神经网络

# 分解出5个领域对象来实现神经网络：
#
# Network 神经网络对象，提供API接口。它由若干层对象组成以及连接对象组成。
# Layer 层对象，由多个节点组成。
# Node 节点对象计算和记录节点自身的信息(比如输出值、误差项等)，以及与这个节点相关的上下游的连接。
# Connection 每个连接对象都要记录该连接的权重。
# Connections 仅仅作为Connection的集合对象，提供一些集合操作。


def sigmoid(inX):
    # print("inX:" + str(inX))
    y = 1.0 / (1 + exp(-inX))
    # if inX > 50000:
    #     print(inX)
    # print("y:" + str(y))
    return y
# def sigmoid(inX):
#     return longfloat( 1.0/(1+exp(-inX)))


# 节点类，负责记录和维护节点自身信息以及与这个节点相关的上下游连接，实现输出值和误差项的计算。
class Node(object):
    def __init__(self, layer_index, node_index):
        '''
        构造节点对象。
        layer_index: 节点所属的层的编号
        node_index: 节点的编号
        '''
        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):
        '''
        设置节点的输出值。如果节点属于输入层会用到这个函数。
        '''
        self.output = output

    def append_downstream_connection(self, conn):
        '''
        添加一个到下游节点的连接
        '''
        self.downstream.append(conn)

    def append_upstream_connection(self, conn):
        '''
        添加一个到上游节点的连接
        '''
        self.upstream.append(conn)

    def calc_output(self):
        '''
        根据式1计算节点的输出
        '''
        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):
        '''
        节点属于隐藏层时，根据式4计算delta
        '''
        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):
        '''
        节点属于输出层时，根据式3计算delta
        '''
        self.delta = self.output * (1 - self.output) * (label - self.output)

    def __str__(self):
        '''
        打印节点的信息
        '''
        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


# ConstNode对象，为了实现一个输出恒为1的节点(计算偏置项时需要)
class ConstNode(object):
    def __init__(self, layer_index, node_index):
        '''
        构造节点对象。
        layer_index: 节点所属的层的编号
        node_index: 节点的编号
        '''
        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


# Layer对象，负责初始化一层。此外，作为Node的集合对象，提供对Node集合的操作。
class Layer(object):
    def __init__(self, layer_index, node_count):
        '''
        初始化一层
        layer_index: 层编号
        node_count: 层所包含的节点个数
        '''
        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):
        '''
        设置层的输出。当层是输入层时会用到。
        '''
        for i in range(len(data)):
            self.nodes[i].set_output(data[i])

    def calc_output(self):
        '''
        计算层的输出向量
        '''
        for node in self.nodes[:-1]:
            node.calc_output()

    def dump(self):
        '''
        打印层的信息
        '''
        for node in self.nodes:
            print(node)


# Connection对象，主要职责是记录连接的权重，以及这个连接所关联的上下游节点。
class Connection(object):
    def __init__(self, upstream_node, downstream_node):
        '''
                初始化连接，权重初始化为是一个很小的随机数
                upstream_node: 连接的上游节点
                downstream_node: 连接的下游节点
                '''
        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):
        '''
                计算梯度
                '''
        self.gradient = self.downstream_node.delta * self.upstream_node.output

    def update_weight(self, rate):
        '''
                根据梯度下降算法更新权重
                '''
        self.calc_gradient()
        self.weight += rate * self.gradient

    def get_gradient(self):
        '''
                获取当前的梯度
                '''
        return self.gradient

    def __str__(self):
        '''
                打印连接信息
                '''
        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)


# Connections对象，提供Connection集合操作。
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)


# Network对象，提供API。
class Network(object):
    def __init__(self, layers):
        '''
                初始化一个全连接神经网络
                layers: 二维数组，描述神经网络每层节点数
                '''
        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):
        '''
                训练神经网络
                labels: 数组，训练样本标签。每个元素是一个样本的标签。
                data_set: 二维数组，训练样本特征。每个元素是一个样本的特征。
                '''
        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):
        '''
                内部函数，用一个样本训练网络
                '''
        self.predict(sample)
        self.calc_delta(label)
        self.update_weight(rate)

    def calc_delta(self, label):
        '''
                内部函数，计算每个节点的delta
                '''
        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):
        '''
                内部函数，更新每个连接权重
                '''
        for layer in self.layers[:-1]:
            for node in layer.nodes:
                for conn in node.downstream:
                    conn.update_weight(rate)

    def calc_gradient(self):
        '''
                内部函数，计算每个连接的梯度
                '''
        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):
        '''
                获得网络在一个样本下，每个连接上的梯度
                label: 样本标签
                sample: 样本输入
                '''
        self.predict(sample)
        self.calc_delta(label)
        self.calc_gradient()

    def predict(self, sample):
        '''
                根据输入的样本预测输出值
                sample: 数组，样本的特征，也就是网络的输入向量
                '''
        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):
        '''
                打印网络信息
                '''
        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 list(map(lambda m: 0.9 if number & m else 0.1, self.mask))

    def denorm(self, vec):
        binary = list(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)
                            )
                        )


# 利用梯度检查来确认程序是否正确
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)
    print("\n gradient_check_test:")
    gradient_check_test()