3. Classification problems - initial experience of handwritten digit recognition

Classification problem introduction

MNIST

The size of each picture is 28*28
matrix [28,28]->[784]->[1,784], Two dimensions become one dimension .

loss

H3：[1,1], first 1 Is the number of pictures , the second 1 Express 0-9 The number of
Y：[0/1/,/9], use one_hot, If its label is 3->[0,0,0,3,0,0,0,0,0]
Suppose the number on the picture is 5, be H3 May be [0.1,0.0.01,0.01,0.03,0.01,0.8,0.01,0.01,0.01,0.01], Actually Y Should be [0,0,0,0,0,1,0,0,0,0].

H3	0.1	0.01	0.01	0.03	0.01	0.8	0.01	0.01	0.01	0.01
Y	0	0	0	0	0	1	0	0	0	0

loss Use Euclidean distance formula to calculate

gradient descent

H1=relu(W1x+b1)
H2=relu(W2H1+b2)
H3=W3*H2+b3
pred=H3
out = Σ(pred-Y)**2

result

argmax(pred)： The maximum value returns the index

First experience of handwritten digits

1. Data loading （Load data）

batch_size = 512
train_loader = torch.utils.data.DataLoader(
    torchvision.datasets.MNIST('mnist_data', train=True, download=True,
                               transform=torchvision.transforms.Compose([
                                   torchvision.transforms.ToTensor(),
                                   torchvision.transforms.Normalize(
                                       (0.1307,), (0.3081,))
                               ])),
    batch_size=batch_size, shuffle=True)
#  hold numpy Format to tensor
#  Regularization , stay 0 near , Can improve performance 
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)

x, y = next(iter(train_loader))
print(x.shape, y.shape, x.min(), x.max())
plot_image(x, y, 'image sample')

2. Creating models （Build Model）

class Net(nn.Module):

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

        #wx+b
        self.fc1 = nn.Linear(28*28,256)  #,28*28 yes x Dimensions ,256 It is generally decided randomly based on experience , The big dimension becomes the small dimension 
        self.fc2 = nn.Linear(256,64)     # The input of the second layer is the same as the output of the previous layer 
        self.fc3 = nn.Linear(64,10)      #10 classification , This is not based on experience 

    # The calculation process 
    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, The last layer adds activation functions according to the situation 
        x = self.fc3(x)

        return x

3. Training （Train）

#train
#net.parameters() return [w1,b1,w2,b2,w3,b3], This is what we need to optimize ; lr It's a learning step  ;momentum Help better optimize 
net = Net()
optimizer = optim.SGD(net.parameters(),lr=0.01,momentum=0.9)

# hold loss Save up 
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] Make it even [b,feature],size(0) yes batch
        x = x.view(x.size(0),28*28)
        # become [b,10]
        out = net(x)
        # [b,10], Actual y
        y_onehot= one_hot(y)
        # loss=mse(out,y_onehot), Find its mean square deviation 
        loss = F.mse_loss(out,y_onehot)

        # Zero gradient 
        optimizer.zero_grad()
        # Calculate the gradient 
        loss.backward()
        #  Update gradient ：w‘ = w-lr*grad
        optimizer.step()

        # Visualize gradient descent , Record the data 
        train_loss.append(loss.item())

        if batch_idx % 10 == 0:
            print(epoch,batch_idx,loss.item())

plot_curve(train_loss)
#we can get optimal [w1,b1,w2,b2,w3,b3]

4. test （Test）

total_correct = 0
for x,y in test_loader:
    x = x.view(x.size(0),28*28)
    #out : [b,10]
    out = net(x)
    #out -> pred:[b]
    pred =out.argmax(dim=1)
    # The sum of the number of current forecast pairs is converted to float, At this time or tensor type , Then convert to numeric type 
    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')