深度学习初探/01-回归问题/3-手写数字识别

深度学习初探/01-回归问题/3-手写数字识别

一、MNIST数据集

MNIST数据集中，有0~9共10个数字的图像数据；每个数字有7k张图片(train/test splitting：6k vs 1k)，每张图片采用28px*28px的矩阵格式存储；每个像素点取值为[0,1]，表示灰度值(0白，1黑)。
对于每张图片，都进行【flat平坦化】操作，使其由二维转为一维，即矩阵由$[28,28]\Rightarrow [1,784]$。

flat平坦化的优点：忽略了二维矩阵的“位置相关性”(上下左右)，更利于处理

二、手写数字识别问题实现步骤:Load data $\Rightarrow$ Build Model $\Rightarrow$ Train $\Rightarrow$ Test

Step0：import一些工具包

import torch
from torch import nn    # nn用于完成神经网络相关的工作
from torch.nn import functional as F  # 常用函数库
from torch import optim  # 优化工具包

import torchvision  # 视觉工具包
from matplotlib import  pyplot as plt  # 绘图工具包

from utils import plot_image,plot_curve,one_hot

Step1：Load data

# Step1:Load Data  加载mnist数据集
# 加载训练集train
train_loader = torch.utils.data.DataLoader(

    torchvision.datasets.MNIST('mnist_data',  # 指定mnist数据集的下载路径
                               train=True,  # 指定下载的数据集是60k的train部分 or 10k的test部分
                               download=True,   # True：若当前文件中没有mnist文件，则自动从网上拉取
                               transform=torchvision.transforms.Compose([
                                   torchvision.transforms.ToTensor(), # 将Numpy格式的文件转换为Tensor
                                   torchvision.transforms.Normalize((0.1307,), (0.3081,))  # 正则化处理，不必要，但可以适当提高性能
                                   # 因为像素点的灰度值x in [0,1]，始终在0右侧
                                   # 故对x进行正则化处理，令(x - 0.1307)/0.3081，保证数据分布在0附近均匀分布，便于神经网络进行优化
                               ])),
    batch_size=batch_size,
    shuffle=True   # 加载时进行“随机打散”
)
# 加载测试集test
test_loader = torch.utils.data.DataLoader(
    torchvision.datasets.MNIST('mnist_data/',
                               train=False,
                               download=True,
                               transform=torchvision.transforms.Compose([
                                   torchvision.transforms.ToTensor(),
                                   torchvision.transforms.Normalize((0.1307,), (0.3081,))
                               ])),
    batch_size=batch_size,
    shuffle=False
)

Step2：Build Model

三层非线性层嵌套网络：在线性模型基础上添加激活函数ReLu

H1 = relu(XW1 + b1)
H2 = relu(H1W2 + b2)
H3 = f (H2W3 + b3)

# Step2：Build Model
class Net(nn.Module):

    def __init__(self):
        super(Net, self).__init__()

        # xw+b
        self.fc1 = nn.Linear(28*28, 256)
        self.fc2 = nn.Linear(256, 64)
        self.fc3 = nn.Linear(64, 10)

    def forward(self, x):
        # x: [b, 1, 28, 28]
        # h1 = relu(xw1+b1)
        x = F.relu(self.fc1(x))
        # h2 = relu(h1w2+b2)
        x = F.relu(self.fc2(x))
        # h3 = h2w3+b3
        x = self.fc3(x)

        return x

Step3：Train

# Step3:Train
net = Net()
# [w1, b1, w2, b2, w3, b3]
optimizer = optim.SGD(net.parameters(), lr=0.01, momentum=0.9)
train_loss = []

for epoch in range(3):

    for batch_idx, (x, y) in enumerate(train_loader):

        # x: [b, 1, 28, 28], y: [512]
        # [b, 1, 28, 28] => [b, 784]
        x = x.view(x.size(0), 28*28)
        # => [b, 10]
        out = net(x)
        # [b, 10]
        y_onehot = one_hot(y)
        # loss = mse(out, y_onehot)
        loss = F.mse_loss(out, y_onehot)

        optimizer.zero_grad()
        loss.backward()
        # w' = w - lr*grad
        optimizer.step()

        train_loss.append(loss.item())

        if batch_idx % 10==0:
            print(epoch, batch_idx, loss.item())
# 可视化梯度下降过程
plot_curve(train_loss)
# we get optimal [w1, b1, w2, b2, w3, b3]

Step4：Test

# Step4:Test
total_correct = 0
for x,y in test_loader:
    x  = x.view(x.size(0), 28*28)
    out = net(x)
    # out: [b, 10] => pred: [b]
    pred = out.argmax(dim=1)
    correct = pred.eq(y).sum().float().item()
    total_correct += correct

total_num = len(test_loader.dataset)
acc = total_correct / total_num
print('test acc:', acc)

x, y = next(iter(test_loader))
out = net(x.view(x.size(0), 28*28))
pred = out.argmax(dim=1)
plot_image(x, pred, 'test')