前言

训练时读入的是.mat格式的训练集，测试正确率时用的是png格式的图片

代码

#!/usr/bin/env python3
# coding=utf-8
import math
import sys
import os
import numpy as np
from PIL import Image
import scipy.io as sio


def sigmoid(x):
    return np.array(list(map(lambda i: 1 / (1 + math.exp(-i)), x)))


def get_train_pattern():
    # 返回训练集的特征和标签
    # current_dir = os.getcwd()
    current_dir = "/home/lxp/F/developing_folder/intelligence_system/bpneuralnet/"
    train = sio.loadmat(current_dir + "mnist_train.mat")["mnist_train"]
    train_label = sio.loadmat(
            current_dir + "mnist_train_labels.mat")["mnist_train_labels"]
    train = np.where(train > 180, 1, 0)  # 二值化
    return train, train_label


def get_test_pattern():
    # 返回测试集
    # base_url = os.getcwd() + "/test/"
    base_url = "/home/lxp/F/developing_folder/intelligence_system/bpneuralnet/mnist_test/"
    test_img_pattern = []
    for i in range(10):
        img_url = os.listdir(base_url + str(i))
        t = []
        for url in img_url:
            img = Image.open(base_url + str(i) + "/" + url)
            img = img.convert('1')  # 二值化
            img_array = np.asarray(img, 'i')  # 转化为int数组
            img_vector = img_array.reshape(
                    img_array.shape[0] * img_array.shape[1])  # 展开成一维数组
            t.append(img_vector)
        test_img_pattern.append(t)
    return test_img_pattern


class BPNetwork:
    # 神经网络类
    def __init__(self, in_count, hiden_count, out_count, in_rate, hiden_rate):
        """

        :param in_count:        输入层数
        :param hiden_count:     隐藏层数
        :param out_count:       输出层数
        :param in_rate:         输入层学习率
        :param hiden_rate:      隐藏层学习率
        """
        # 各个层的节点数量
        self.in_count = in_count
        self.hiden_count = hiden_count
        self.out_count = out_count

        # 输入层到隐藏层连线的权重随机初始化
        self.w1 = 0.2 * \
                np.random.random((self.in_count, self.hiden_count)) - 0.1

        # 隐藏层到输出层连线的权重随机初始化
        self.w2 = 0.2 * \
                np.random.random((self.hiden_count, self.out_count)) - 0.1

        # 隐藏层偏置向量
        self.hiden_offset = np.zeros(self.hiden_count)
        # 输出层偏置向量
        self.out_offset = np.zeros(self.out_count)

        # 输入层学习率
        self.in_rate = in_rate
        # 隐藏层学习率
        self.hiden_rate = hiden_rate

    def train(self, train_img_pattern, train_label):
        if self.in_count != len(train_img_pattern[0]):
            sys.exit("输入层维数与样本维数不等")
        # for num in range(10):
        # for num in range(10):
        for i in range(len(train_img_pattern)):
            if i % 5000 == 0:
                print(i)
            # 生成目标向量
            target = [0] * 10
            target[train_label[i][0]] = 1
            # for t in range(len(train_img_pattern[num])):
            # 前向传播
            # 隐藏层值等于输入层*w1+隐藏层偏置
            hiden_value = np.dot(
                    train_img_pattern[i], self.w1) + self.hiden_offset
            hiden_value = sigmoid(hiden_value)

            # 计算输出层的输出
            out_value = np.dot(hiden_value, self.w2) + self.out_offset
            out_value = sigmoid(out_value)

            # 反向更新
            error = target - out_value
            # 计算输出层误差
            out_error = out_value * (1 - out_value) * error
            # 计算隐藏层误差
            hiden_error = hiden_value * \
                    (1 - hiden_value) * np.dot(self.w2, out_error)

            # 更新w2，w2是j行k列的矩阵，存储隐藏层到输出层的权值
            for k in range(self.out_count):
                # 更新w2第k列的值，连接隐藏层所有节点到输出层的第k个节点的边
                # 隐藏层学习率×输入层误差×隐藏层的输出值
                self.w2[:, k] += self.hiden_rate * out_error[k] * hiden_value

            # 更新w1
            for j in range(self.hiden_count):
                self.w1[:, j] += self.in_rate * \
                        hiden_error[j] * train_img_pattern[i]

            # 更新偏置向量
            self.out_offset += self.hiden_rate * out_error
            self.hiden_offset += self.in_rate * hiden_error

    def test(self, test_img_pattern):
        """
        测试神经网络的正确率
        :param test_img_pattern[num][t]表示数字num的第t张图片
        :return:
        """
        right = np.zeros(10)
        test_sum = 0
        for num in range(10):  # 10个数字
            # print("正在识别", num)
            num_count = len(test_img_pattern[num])
            test_sum += num_count
            for t in range(num_count):  # 数字num的第t张图片
                hiden_value = np.dot(
                        test_img_pattern[num][t], self.w1) + self.hiden_offset
                hiden_value = sigmoid(hiden_value)
                out_value = np.dot(hiden_value, self.w2) + self.out_offset
                out_value = sigmoid(out_value)
                # print(out_value)
                if np.argmax(out_value) == num:
                    # 识别正确
                    right[num] += 1
            print("数字%d的识别正确率%f" % (num, right[num] / num_count))

        # 平均识别率
        print("平均识别率为：", sum(right) / test_sum)

    """
    def test1:


    """


def run():
    # 读入训练集
    train, train_label = get_train_pattern()

    # 读入测试图片
    test_pattern = get_test_pattern()

    # 神经网络配置参数
    in_count = 28 * 28
    hiden_count = 6
    out_count = 10
    in_rate = 0.1
    hiden_rate = 0.1
    bpnn = BPNetwork(in_count, hiden_count, out_count, in_rate, hiden_rate)
    bpnn.train(train, train_label)
    bpnn.test(test_pattern)

    # 单张测试
    # 识别单独一张图片，返回识别结果
    """
    while True:
        img_name = input("输入要识别的图片\n")
        base_url = "/home/lxp/F/developing_folder/intelligence_system/bpneuralnet/"
        img_url = base_url + img_name
        img = Image.open(img_url)
        img = img.convert('1')  # 二值化
        img_array = np.asarray(img, 'i')  # 转化为int数组
        # 得到图片的特征向量
        img_v = img_array.reshape(img_array.shape[0] * img_array.shape[1])  # 展开成一维数组
        bpnn.test1(img_v)

    """


if __name__ == "__main__":
    run()
    # train, train_label = get_train_pattern()
    # print(train_label[5][0])
# test = get_test_pattern()

数据集下载： 链接: https://pan.baidu.com/s/1ldWTSqVUm6l1cc4EDOzHpQ 提取码: mm93