陕西公路工程建设有限公司网站,产品推广计划,商业网站开发实训内容,网页游戏排行榜奇迹第四章.误差反向传播法 4.3 误差反向传播法实现手写数字识别神经网络 通过像组装乐高积木一样组装第四章中实现的层#xff0c;来构建神经网络。 1.神经网络学习全貌图 1).前提#xff1a;
神经网络存在合适的权重和偏置#xff0c;调整权重和偏置以便拟合训练数据的过程称… 第四章.误差反向传播法 4.3 误差反向传播法实现手写数字识别神经网络 通过像组装乐高积木一样组装第四章中实现的层来构建神经网络。 1.神经网络学习全貌图 1).前提
神经网络存在合适的权重和偏置调整权重和偏置以便拟合训练数据的过程称为“学习”神经网络的学习分成下面4个步骤。 2).步骤1 (mini-batch):
从训练数据中随机选出一部分数据这部分数据称为mini-batch,我们的目标是减少mini-batch损失函数的值。 3).步骤2 (计算梯度):
为了减少mini_batch损失函数的值需要求出各个权重参数的梯度梯度表示损失函数的值减少最多的方向。 4).步骤3 (更新参数):
将权重参数沿梯度方向进行微小更新 5).步骤4 (重复)
重复步骤1步骤2步骤3
2.手写数字识别神经网络的实现:(2层)
# 误差反向传播法实现手写数字识别神经网络import numpy as np
import matplotlib.pyplot as plt
import sys, ossys.path.append(os.pardir)
from dataset.mnist import load_mnist
from collections import OrderedDictclass Affine:def __init__(self, W, b):self.W Wself.b bself.x Noneself.original_x_shape None# 权重和偏置参数的导数self.dW Noneself.db None# 向前传播def forward(self, x):self.original_x_shape x.shapex x.reshape(x.shape[0], -1)self.x xout np.dot(self.x, self.W) self.breturn out# 反向传播def backward(self, dout):dx np.dot(dout, self.W.T)self.dW np.dot(self.x.T, dout)self.db np.sum(dout, axis0)dx dx.reshape(*self.original_x_shape) # 还原输入数据的形状对应张量return dxclass ReLU:def __init__(self):self.mask Nonedef forward(self, x):self.mask (x 0)out x.copy()out[self.mask] 0return outdef backward(self, dout):dout[self.mask] 0dx doutreturn dxclass SoftmaxWithLoss:def __init__(self):self.loss Noneself.y Noneself.t None# 输出层函数softmaxdef softmax(self, x):if x.ndim 2:x x.Tx x - np.max(x, axis0)y np.exp(x) / np.sum(np.exp(x), axis0)return y.Tx x - np.max(x) # 溢出对策y np.exp(x) / np.sum(np.exp(x))return y# 误差函数交叉熵误差def cross_entropy_error(self, y, t):if y.ndim 1:y y.reshape(1, y.size)t t.reshape(1, t.size)# 监督数据是one_hot_label的情况下转换为正确解标签的索引if t.size y.size:t t.argmax(axis1)batch_size y.shape[0]return -np.sum(np.log(y[np.arange(batch_size), t] 1e-7)) / batch_sizedef forward(self, x, t):self.t tself.y self.softmax(x)self.loss self.cross_entropy_error(self.y, self.t)return self.lossdef backward(self, dout1):batch_size self.t.shape[0]if self.t.size self.y.size:dx (self.y - self.t) / batch_sizeelse:dx self.y.copy()dx[np.arange(batch_size), self.t] - 1dx dx / batch_sizereturn dxclass TwoLayerNet:# 初始化def __init__(self, input_size, hidden_size, output_size, weight_init_std0.01):# 初始化权重self.params {}self.params[W1] weight_init_std * np.random.randn(input_size, hidden_size)self.params[b1] np.zeros(hidden_size)self.params[W2] weight_init_std * np.random.randn(hidden_size, output_size)self.params[b2] np.zeros(output_size)# 生成层self.layers OrderedDict()self.layers[Affine1] Affine(self.params[W1], self.params[b1])self.layers[ReLU] ReLU()self.layers[Affine2] Affine(self.params[W2], self.params[b2])self.lastLayer SoftmaxWithLoss()def predict(self, x):for layer in self.layers.values():x layer.forward(x)return xdef loss(self, x, t):y self.predict(x)loss self.lastLayer.forward(y, t)return lossdef accuracy(self, x, t):y self.predict(x)y np.argmax(y, axis1)if t.ndim ! 1: t np.argmax(t, axis1)accuracy np.sum(y t) / float(t.shape[0])return accuracy# 微分函数def numerical_gradient1(self, f, x):h 1e-4grad np.zeros_like(x)it np.nditer(x, flags[multi_index], op_flags[readwrite])while not it.finished:idx it.multi_indextmp_val x[idx]x[idx] float(tmp_val) hfxh1 f(x) # f(xh)x[idx] tmp_val - hfxh2 f(x) # f(x-h)grad[idx] (fxh1 - fxh2) / (2 * h)x[idx] tmp_val # 还原值it.iternext()return grad# 通过数值微分计算关于权重参数的梯度def numerical_gradient(self, x, t):loss_W lambda W: self.loss(x, t)grad {}grad[W1] self.numerical_gradient1(loss_W, self.params[W1])grad[b1] self.numerical_gradient1(loss_W, self.params[b1])grad[W2] self.numerical_gradient1(loss_W, self.params[W2])grad[b2] self.numerical_gradient1(loss_W, self.params[b2])return grad# 通过误差反向传播法计算权重参数的梯度误差def gradient(self, x, t):# 正向传播self.loss(x, t)# 反向传播dout 1dout self.lastLayer.backward(dout)layers list(self.layers.values())layers.reverse()for layer in layers:dout layer.backward(dout)# 设定grads {}grads[W1] self.layers[Affine1].dWgrads[b1] self.layers[Affine1].dbgrads[W2] self.layers[Affine2].dWgrads[b2] self.layers[Affine2].dbreturn grads# 读入数据
def get_data():(x_train, t_train), (x_test, t_test) load_mnist(normalizeTrue, one_hot_labelTrue)return (x_train, t_train), (x_test, t_test)# 读入数据
(x_train, t_train), (x_test, t_test) get_data()network TwoLayerNet(input_size784, hidden_size50, output_size10)iters_num 10000
train_size x_train.shape[0]
batch_size 100
lr 0.1
train_loss_list []
train_acc_list []
test_acc_list []
iter_per_epoch max(train_size / batch_size, 1)for i in range(iters_num):batch_mask np.random.choice(train_size, batch_size)x_batch x_train[batch_mask]t_batch t_train[batch_mask]# 通过误差反向传播法求梯度grad network.gradient(x_batch, t_batch)# 更新for key in (W1, b1, W2, b2):network.params[key] - lr * grad[key]loss network.loss(x_batch, t_batch)train_loss_list.append(loss)if i % iter_per_epoch 0:train_acc network.accuracy(x_train, t_train)train_acc_list.append(train_acc)test_acc network.accuracy(x_test, t_test)test_acc_list.append(test_acc)print(train_acc,test_acc|, str(train_acc) , str(test_acc))# 绘制识别精度图像
plt.rcParams[font.sans-serif] [SimHei] # 解决中文乱码
plt.rcParams[axes.unicode_minus] False # 解决负号不显示的问题plt.figure(figsize(8, 4))
plt.subplot(1, 2, 1)
x_data np.arange(0, len(train_acc_list))
plt.plot(x_data, train_acc_list, b)
plt.plot(x_data, test_acc_list, r)
plt.xlabel(epoch)
plt.ylabel(accuracy)
plt.ylim(0.0, 1.0)
plt.title(训练数据和测试数据的识别精度)
plt.legend([train_acc, test_acc])plt.subplot(1, 2, 2)
x_data np.arange(0, len(train_loss_list))
plt.plot(x_data, train_loss_list, g)
plt.xlabel(iters_num)
plt.ylabel(loss)
plt.title(损失函数)
plt.show()
3.结果展示
