LeNet-5是卷积神经网络模型的早期代表，它由LeCun在1998年提出。该模型采用顺序结构，主要包括7层（2个卷积层、2个池化层和3个全连接层），卷积层和池化层交替排列。以mnist手写数字分类为例构建一个LeNet-5模型。每个手写数字图片样本的宽与高均为28像素，样本标签值是0~9，代表0至9十个数字。
图1. LeNet-5模型
下面详细解析LeNet-5模型的正向传播过程。
（1）卷积层C1C1层的输入数据形状大小为 R 1 × 28 × 28 \mathbb{R}^{1 \times 28 \times 28} R1×28×28，表示通道数量为1，行与列的大小都为28。输出数据形状大小为 R 6 × 24 × 24 \mathbb{R}^{6 \times 24 \times 24} R6×24×24，表示通道数量为6，行与列维都为24。
卷积核。L1层的卷积核形状大小 R 6 × 1 × 5 × 5 \mathbb{R}^{6 \times 1 \times 5 \times 5} R6×1×5×5为，偏置项形状大小为6。
这里有两个问题很关键：一是，为什么通道数从1变成了6呢？原因是模型的卷积层L1设定了6个卷积核，每个卷积核都与输入数据发生运算，最终分别得到6组数据。二是，为什么行列大小从28变成了24呢？原因是每个卷积核的行维与列维都为5，卷积核（5×5）在输入数据（28×28）上移动，且每次移动步长为1，那么输出数据的行列大小分别为28-5+1=24。
（2）池化层S1L2层的输入数据大小要和L1层的输出数据大小保持一致。输入数据形状大小为 R 6 × 24 × 24 \mathbb{R}^{6 \times 24 \times 24} R6×24×24，表示通道数量为6，行与列的大小都为24。L2层的输出数据形状大小为 R 6 × 12 × 12 \mathbb{R}^{6 \times 12 \times 12} R6×12×12，表示通道数量为6，行与列维都为12。
为什么行列大小从24变成了12呢？原因是池化层中的过滤器形状大小为2×2，其在输入数据（24×24）上移动，且每次移动步长（跨距）为2，每次选择4个数（2×2）中最大值作为输出，那么输出数据的行列大小分别为24÷2=12。
（3）卷积层C2L3层的输入数据形状大小为 R 6 × 12 × 12 \mathbb{R}^{6 \times 12 \times 12} R6×12×12，表示通道数量为6，行与列的大小都为12。L3层的输出数据形状大小为 R 16 × 8 × 8 \mathbb{R}^{16 \times 8 \times 8} R16×8×8，表示通道数量为16，行与列维都为8。
卷积核。L3层的卷积核形状大小为 R m × 16 × 6 × 5 × 5 \mathbb{R}^{m \times 16 \times 6 \times 5 \times 5} Rm×16×6×5×5，偏置项形状大小为16。
（4）池化层S2L4层的输入数据形状大小与L3层的输出数据大小一致。L4层的输入数据形状大小为 R 16 × 8 × 8 \mathbb{R}^{16 \times 8 \times 8} R16×8×8，表示通道数量为16，行与列的大小都为8。L4层的输出数据形状大小为 R 16 × 4 × 4 \mathbb{R}^{16 \times 4 \times 4} R16×4×4，表示通道数量为16，行与列维都为4。
（5）卷积层C3由于L5层是线性层，其输入大小为一维，所以需要把L4层的输出数据大小进行重新划分。L4层的输出形状大小为 R 16 × 4 × 4 \mathbb{R}^{16 \times 4 \times 4} R16×4×4，则L5层的一维输入形状大小为16×4×4=256。L4层的一维输出大小为120。
（6）线性层F1L6层的输入特征数量为120。L6层的输出特征数量为84。
（7）线性层F2L7层的输入特征数量为84。L7层的输出特征数量为10。 由于是分类问题，我们选择交叉熵损失函数。交叉熵主要用于衡量估计值与真实值之间的差距。交叉熵值越小，模型预测效果越好。
E ( y i , y ^ i ) = − ∑ j = 1 q y j i l n ( y ^ j i ) E(\mathbf{y}^{i},\mathbf{\hat{y}}^{i})=-\sum_{j=1}^{q}\mathbf{y}_{j}^{i}ln(\mathbf{\hat{y}}_{j}^{i}) E(yi,y^i)=−j=1∑qyjiln(y^ji)
其中， y i ∈ R q \mathbf{y}^{i} \in \mathbb{R}^{q} yi∈Rq为真实值， y j i y_{j}^{i} yji是 y i \mathbf{y}^{i} yi中的元素(取值为0或1)， j = 1 , . . . , q j=1,...,q j=1,...,q。 y ^ i ∈ R q \mathbf{\hat{y}^{i}} \in \mathbb{R}^{q} y^i∈Rq是预测值（样本在每个类别上的概率）。
定义好了正向传播过程之后，接着随机化初始参数，然后便可以计算出每层的结果，每次将得到m×10的矩阵作为预测结果，其中m是小批量样本数。接下来进行反向传播过程，预测结果与真实结果之间肯定存在差异，以缩减该差异作为目标，计算模型参数梯度。进行多轮迭代，便可以优化模型，使得预测结果与真实结果之间更加接近。
1. 数据的下载 from torchvision.datasets import MNISTimport torchimport torchvision.transforms as transformstrain_dataset=MNIST(root="./data/",train=True,transform=transforms.ToTensor(),download=True)test_dataset=MNIST(root="./data/",train=False,transform=transforms.ToTensor()) len(train_dataset),len(test_dataset) (60000, 10000) train_dataset[0][0].shape torch.Size([1, 28, 28]) train_dataset[0][0].shape torch.Size([1, 28, 28]) train_dataset[0][1] 5 2. 定义模型 from torch import nn nn.Conv2d? class Lenet5(nn.Module):def __init__(self):super(Lenet5,self).__init__()#1+ 28-5/(1)==24self.features=nn.Sequential(#定义第一个卷积层nn.Conv2d(in_channels=1,out_channels=6,kernel_size=(5,5),stride=1),nn.ReLU(),nn.AvgPool2d(kernel_size=2,stride=2),#6*12*12#定义第二个卷积层nn.Conv2d(in_channels=6,out_channels=16,kernel_size=(5,5),stride=1),#1+12-5/(1)=16*8*8nn.ReLU(),nn.MaxPool2d(kernel_size=2,stride=2),#1+(8-2)/(2)=4#16*4*4)#定义全连接层self.classfier=nn.Sequential(nn.Linear(in_features=256,out_features=120),nn.ReLU(),nn.Linear(in_features=120,out_features=84),nn.ReLU(),nn.Linear(in_features=84,out_features=10), )def forward(self,x):x=self.features(x)x=torch.flatten(x,1)result=self.classfier(x)return result 3. 新建模型 model=Lenet5()device=torch.device("cuda:0" if torch.cuda.is_available() else "cpu")model=model.to(device) 4. 从数据集中分批量读取数据 from torch.utils.data import DataLoader DataLoader? from torch.utils.data import DataLoaderbatch_size=32train_loader=DataLoader(dataset=train_dataset,batch_size=batch_size,shuffle=True)test_loader=DataLoader(dataset=test_dataset,batch_size=batch_size,shuffle=False) 5. 定义损失函数 from torch import optim loss_fun=nn.CrossEntropyLoss()loss_lst=[] 6. 定义优化器 optimizer=optim.SGD(params=model.parameters(),lr=0.001,momentum=0.9) 7. 开始训练 import timestart_time=time.time()#训练的迭代次数for i in range(10):loss_i=0for j,(batch_data,batch_label) in enumerate(train_loader):#清空优化器的梯度optimizer.zero_grad()#模型前向预测pred=model(batch_data)loss=loss_fun(pred,batch_label)loss_i+=lossloss.backward()optimizer.step()if (j+1)%200==0:print("第%d次训练，第%d批次，损失为%.2f"%(i,j,loss_i/200))loss_i=0end_time=time.time()print("共训练了%d 秒"%(end_time-start_time)) 第0次训练，第199批次，损失为2.30第0次训练，第399批次，损失为2.29第0次训练，第599批次，损失为2.28第0次训练，第799批次，损失为2.23第0次训练，第999批次，损失为1.86第0次训练，第1199批次，损失为0.81第0次训练，第1399批次，损失为0.55第0次训练，第1599批次，损失为0.46第0次训练，第1799批次，损失为0.40第1次训练，第199批次，损失为0.33第1次训练，第399批次，损失为0.29第1次训练，第599批次，损失为0.27第1次训练，第799批次，损失为0.28第1次训练，第999批次，损失为0.25第1次训练，第1199批次，损失为0.22第1次训练，第1399批次，损失为0.23第1次训练，第1599批次，损失为0.22第1次训练，第1799批次，损失为0.19第2次训练，第199批次，损失为0.17第2次训练，第399批次，损失为0.17第2次训练，第599批次，损失为0.16第2次训练，第799批次，损失为0.17第2次训练，第999批次，损失为0.15第2次训练，第1199批次，损失为0.15第2次训练，第1399批次，损失为0.14第2次训练，第1599批次，损失为0.14第2次训练，第1799批次，损失为0.13第3次训练，第199批次，损失为0.12第3次训练，第399批次，损失为0.13第3次训练，第599批次，损失为0.12第3次训练，第799批次，损失为0.12第3次训练，第999批次，损失为0.13第3次训练，第1199批次，损失为0.12第3次训练，第1399批次，损失为0.10第3次训练，第1599批次，损失为0.11第3次训练，第1799批次，损失为0.10第4次训练，第199批次，损失为0.11第4次训练，第399批次，损失为0.10第4次训练，第599批次，损失为0.10第4次训练，第799批次，损失为0.08第4次训练，第999批次，损失为0.09第4次训练，第1199批次，损失为0.09第4次训练，第1399批次，损失为0.10第4次训练，第1599批次，损失为0.08第4次训练，第1799批次，损失为0.08第5次训练，第199批次，损失为0.09第5次训练，第399批次，损失为0.07第5次训练，第599批次，损失为0.09第5次训练，第799批次，损失为0.08第5次训练，第999批次，损失为0.08第5次训练，第1199批次，损失为0.08第5次训练，第1399批次，损失为0.08第5次训练，第1599批次，损失为0.07第5次训练，第1799批次，损失为0.08第6次训练，第199批次，损失为0.08第6次训练，第399批次，损失为0.07第6次训练，第599批次，损失为0.07第6次训练，第799批次，损失为0.07第6次训练，第999批次，损失为0.08第6次训练，第1199批次，损失为0.07第6次训练，第1399批次，损失为0.07第6次训练，第1599批次，损失为0.07第6次训练，第1799批次，损失为0.08第7次训练，第199批次，损失为0.07第7次训练，第399批次，损失为0.07第7次训练，第599批次，损失为0.07第7次训练，第799批次，损失为0.06第7次训练，第999批次，损失为0.07第7次训练，第1199批次，损失为0.06第7次训练，第1399批次，损失为0.06第7次训练，第1599批次，损失为0.07第7次训练，第1799批次，损失为0.06第8次训练，第199批次，损失为0.05第8次训练，第399批次，损失为0.05第8次训练，第599批次，损失为0.06第8次训练，第799批次，损失为0.06第8次训练，第999批次，损失为0.07第8次训练，第1199批次，损失为0.06第8次训练，第1399批次，损失为0.07第8次训练，第1599批次，损失为0.06第8次训练，第1799批次，损失为0.05第9次训练，第199批次，损失为0.05第9次训练，第399批次，损失为0.05第9次训练，第599批次，损失为0.05第9次训练，第799批次，损失为0.05第9次训练，第999批次，损失为0.05第9次训练，第1199批次，损失为0.06第9次训练，第1399批次，损失为0.05第9次训练，第1599批次，损失为0.05第9次训练，第1799批次，损失为0.05共训练了148 秒 8. 测试和保存模型 len(test_dataset) 10000 correct=0for batch_data,batch_label in test_loader:pred_test=model(batch_data)pred_result=torch.max(pred_test.data,1)[1]correct+=(pred_result==batch_label).sum()print("准确率为:%.2f%%"%(correct/len(test_dataset))) 准确率为:0.98% #保存模型torch.save(model, './model-cifar10.pth') 9. 手写体图片的可视化 from torchvision import transforms as T import torch import numpy as npfrom PIL import Imagenormalize = T.Normalize(mean=[127.5, 127.5, 127.5], std=[127.5, 127.5, 127.5])arr1=np.random.rand(300, 320, 3) * 255fake_img = T.ToPILImage()(arr1.astype("uint8"))fake_img.show()fake_img = normalize(T.ToTensor()(arr1))print(fake_img.shape)print(fake_img) torch.Size([3, 300, 320])tensor([[[-0.9172, -0.8087, 0.5650, ..., 0.5297, 0.8186, 0.3312],[-0.3795, -0.7144, 0.7482, ..., 0.7777, 0.0563, 0.9862],[ 0.4713, 0.1514, 0.1433, ..., 0.1218, 0.5960, 0.0122],...,[ 0.7886, -0.8431, 0.2048, ..., 0.0880, 0.8566, -0.7309],[-0.5249, -0.2610, 0.6604, ..., -0.5265, -0.8607, 0.8407],[-0.0764, -0.6659, -0.7282, ..., 0.6114, -0.8531, 0.8591]],[[-0.7804, -0.9011, 0.7292, ..., -0.7269, 0.4730, -0.4985],[ 0.5025, -0.9715, -0.5368, ..., -0.3784, 0.2336, -0.7914],[-0.3683, 0.5105, 0.4923, ..., 0.4562, 0.1588, 0.0781],...,[-0.7712, 0.4029, 0.5997, ..., 0.6086, -0.6148, 0.8007],[ 0.9939, 0.0161, -0.9449, ..., -0.6050, -0.3625, 0.0129],[-0.2682, -0.1006, -0.7786, ..., 0.0569, 0.0279, -0.3509]],[[-0.9476, 0.3883, 0.4793, ..., -0.2685, 0.9854, 0.9068],[ 0.4380, 0.1821, -0.1389, ..., -0.8316, 0.5408, -0.2924],[-0.3324, -0.8534, -0.9868, ..., -0.8449, -0.3564, -0.9859],...,[ 0.9973, 0.4672, -0.4873, ..., -0.5094, -0.6851, 0.2794],[ 0.9954, 0.8549, 0.1814, ..., -0.7077, -0.7606, 0.4524],[ 0.6209, 0.5317, -0.1966, ..., -0.8245, -0.8593, -0.1789]]],dtype=torch.float64) len(train_dataset) 60000 train_dataset[0][0].shape torch.Size([1, 28, 28]) import matplotlib.pyplot as pltplt.imshow(train_dataset[3][0][0],cmap="gray") <matplotlib.image.AxesImage at 0x217dc3c6bd0> 10. 多幅图片的可视化 from matplotlib import pyplot as pltplt.figure(figsize=(20,15))cols=10rows=10for i in range(0,rows):for j in range(0,cols):idx=j+i*colsplt.subplot(rows,cols,idx+1) plt.imshow(train_dataset[idx][0][0])plt.axis('off') import numpy as npimg10 = np.stack(list(train_dataset[i][0][0] for i in range(10)), axis=1).reshape(28,280)plt.imshow(img10)plt.axis('off') (-0.5, 279.5, 27.5, -0.5) img100 = np.stack(tuple(np.stack(tuple(train_dataset[j*10+i][0][0] for i in range(10)), axis=1).reshape(28,280) for j in range(10)),axis=0).reshape(280,280)plt.imshow(img100)plt.axis('off') (-0.5, 279.5, 279.5, -0.5) 思考题 测试集中有哪些识别错误的手写数字图片？ 汇集整理并分析原因？ 11. 读取测试集的图片预测值（神经网络的输出为10） #导入模型model1=torch.load('./model-cifar10.pth') pre_result=torch.zeros(len(test_dataset),10)for i in range(len(test_dataset)):pre_result[i,:]=model1(torch.reshape(test_dataset[i][0],(-1,1,28,28)))pre_result tensor([[-1.8005, -0.1725, 1.4765, ..., 13.5399, -0.6261, 3.8320],[ 4.3233, 7.6017, 16.5872, ..., -0.0560, 5.2066, -7.0792],[-2.1821, 9.3779, 0.7749, ..., 1.8749, 1.6951, -2.9422],...,[-5.5755, -2.2075, -9.2250, ..., -0.2451, 3.3703, 1.2951],[ 0.5491, -7.7018, -5.8288, ..., -7.6734, 9.3946, -1.9603],[ 3.5516, -8.2659, -0.5965, ..., -8.5934, 1.0133, -2.2048]],grad_fn=<CopySlices>) pre_result.shape torch.Size([10000, 10]) pre_result[:5] tensor([[-1.8005e+00, -1.7254e-01, 1.4765e+00, 3.0824e+00, -2.5454e+00,-7.6911e-01, -1.2368e+01, 1.3540e+01, -6.2614e-01, 3.8320e+00],[ 4.3233e+00, 7.6017e+00, 1.6587e+01, 3.6477e+00, -6.6674e+00,-6.0579e+00, -1.5660e+00, -5.5983e-02, 5.2066e+00, -7.0792e+00],[-2.1821e+00, 9.3779e+00, 7.7487e-01, -3.0049e+00, 1.3374e+00,-1.6613e+00, 8.8544e-01, 1.8749e+00, 1.6951e+00, -2.9422e+00],[ 1.3456e+01, -9.9020e+00, 2.8586e+00, -2.2105e+00, -1.8515e+00,1.7651e-03, 4.7584e+00, -1.3772e+00, -2.2127e+00, 1.5543e+00],[-2.9573e+00, -2.5707e+00, -3.5142e+00, -1.7487e+00, 1.2020e+01,-8.8355e-01, -1.0698e+00, 6.3823e-01, -3.5542e-01, 3.6258e+00]],grad_fn=<SliceBackward0>) #显示这10000张图片的标签label_10000=[test_dataset[i][1] for i in range(10000)]label_10000 [7,2,1,0,4,1,4,9,5,9,0,6,9,0,1,5,9,7,3,4,9,6,6,5,4,0,7,4,0,1,3,1,3,4,7,2,7,1,2,1,1,7,4,2,3,5,1,2,4,4,6,3,5,5,6,0,4,1,9,5,7,8,9,3,7,4,6,4,3,0,7,0,2,9,1,7,3,2,9,7,7,6,2,7,8,4,7,3,6,1,3,6,9,3,1,4,1,7,6,9,6,0,5,4,9,9,2,1,9,4,8,7,3,9,7,4,4,4,9,2,5,4,7,6,7,9,0,5,8,5,6,6,5,7,8,1,0,1,6,4,6,7,3,1,7,1,8,2,0,2,9,9,5,5,1,5,6,0,3,4,4,6,5,4,6,5,4,5,1,4,4,7,2,3,2,7,1,8,1,8,1,8,5,0,8,9,2,5,0,1,1,1,0,9,0,3,1,6,4,2,3,6,1,1,1,3,9,5,2,9,4,5,9,3,9,0,3,6,5,5,7,2,2,7,1,2,8,4,1,7,3,3,8,8,7,9,2,2,4,1,5,9,8,7,2,3,0,4,4,2,4,1,9,5,7,7,2,8,2,6,8,5,7,7,9,1,8,1,8,0,3,0,1,9,9,4,1,8,2,1,2,9,7,5,9,2,6,4,1,5,8,2,9,2,0,4,0,0,2,8,4,7,1,2,4,0,2,7,4,3,3,0,0,3,1,9,6,5,2,5,9,2,9,3,0,4,2,0,7,1,1,2,1,5,3,3,9,7,8,6,5,6,1,3,8,1,0,5,1,3,1,5,5,6,1,8,5,1,7,9,4,6,2,2,5,0,6,5,6,3,7,2,0,8,8,5,4,1,1,4,0,3,3,7,6,1,6,2,1,9,2,8,6,1,9,5,2,5,4,4,2,8,3,8,2,4,5,0,3,1,7,7,5,7,9,7,1,9,2,1,4,2,9,2,0,4,9,1,4,8,1,8,4,5,9,8,8,3,7,6,0,0,3,0,2,6,6,4,9,3,3,3,2,3,9,1,2,6,8,0,5,6,6,6,3,8,8,2,7,5,8,9,6,1,8,4,1,2,5,9,1,9,7,5,4,0,8,9,9,1,0,5,2,3,7,8,9,4,0,6,3,9,5,2,1,3,1,3,6,5,7,4,2,2,6,3,2,6,5,4,8,9,7,1,3,0,3,8,3,1,9,3,4,4,6,4,2,1,8,2,5,4,8,8,4,0,0,2,3,2,7,7,0,8,7,4,4,7,9,6,9,0,9,8,0,4,6,0,6,3,5,4,8,3,3,9,3,3,3,7,8,0,8,2,1,7,0,6,5,4,3,8,0,9,6,3,8,0,9,9,6,8,6,8,5,7,8,6,0,2,4,0,2,2,3,1,9,7,5,1,0,8,4,6,2,6,7,9,3,2,9,8,2,2,9,2,7,3,5,9,1,8,0,2,0,5,2,1,3,7,6,7,1,2,5,8,0,3,7,2,4,0,9,1,8,6,7,7,4,3,4,9,1,9,5,1,7,3,9,7,6,9,1,3,7,8,3,3,6,7,2,8,5,8,5,1,1,4,4,3,1,0,7,7,0,7,9,4,4,8,5,5,4,0,8,2,1,0,8,4,5,0,4,0,6,1,7,3,2,6,7,2,6,9,3,1,4,6,2,5,4,2,0,6,2,1,7,3,4,1,0,5,4,3,1,1,7,4,9,9,4,8,4,0,2,4,5,1,1,6,4,7,1,9,4,2,4,1,5,5,3,8,3,1,4,5,6,8,9,4,1,5,3,8,0,3,2,5,1,2,8,3,4,4,0,8,8,3,3,1,7,3,5,9,6,3,2,6,1,3,6,0,7,2,1,7,1,4,2,4,2,1,7,9,6,1,1,2,4,8,1,7,7,4,8,0,7,3,1,3,1,0,7,7,0,3,5,5,2,7,6,6,9,2,8,3,5,2,2,5,6,0,8,2,9,2,8,8,8,8,7,4,9,3,0,6,6,3,2,1,3,2,2,9,3,0,0,5,7,8,1,4,4,6,0,2,9,1,4,7,4,7,3,9,8,8,4,7,1,2,1,2,2,3,2,3,2,3,9,1,7,4,0,3,5,5,8,6,3,2,6,7,6,6,3,2,7,8,1,1,7,5,6,4,9,5,1,3,3,4,7,8,9,1,1,6,9,1,4,4,5,4,0,6,2,2,3,1,5,1,2,0,3,8,1,2,6,7,1,6,2,3,9,0,1,2,2,0,8,9,...] import numpy as nppre_10000=pre_result.detach()pre_10000 tensor([[-1.8005, -0.1725, 1.4765, ..., 13.5399, -0.6261, 3.8320],[ 4.3233, 7.6017, 16.5872, ..., -0.0560, 5.2066, -7.0792],[-2.1821, 9.3779, 0.7749, ..., 1.8749, 1.6951, -2.9422],...,[-5.5755, -2.2075, -9.2250, ..., -0.2451, 3.3703, 1.2951],[ 0.5491, -7.7018, -5.8288, ..., -7.6734, 9.3946, -1.9603],[ 3.5516, -8.2659, -0.5965, ..., -8.5934, 1.0133, -2.2048]]) pre_10000=np.array(pre_10000)pre_10000 array([[-1.8004757 , -0.17253768, 1.4764961 , ..., 13.539932 ,-0.6261405 , 3.832048 ],[ 4.323273 , 7.601658 , 16.587166 , ..., -0.05598306,5.20656 , -7.0792093 ],[-2.1820781 , 9.377863 , 0.7748679 , ..., 1.8749483 ,1.6950815 , -2.9421623 ],...,[-5.575542 , -2.2075167 , -9.225033 , ..., -0.24509335,3.3702612 , 1.2950805 ],[ 0.5491407 , -7.7017508 , -5.8287773 , ..., -7.6733685 ,9.39456 , -1.9602803 ],[ 3.5516088 , -8.265893 , -0.59651583, ..., -8.593432 ,1.0132635 , -2.2048213 ]], dtype=float32) 12. 采用pandas可视化数据 import pandas as pd table=pd.DataFrame(zip(pre_10000,label_10000))table 010[-1.8004757, -0.17253768, 1.4764961, 3.0824265...71[4.323273, 7.601658, 16.587166, 3.6476722, -6....22[-2.1820781, 9.377863, 0.7748679, -3.0049446, ...13[13.455704, -9.902006, 2.8586285, -2.2104588, ...04[-2.9572597, -2.5707455, -3.5142026, -1.748683...4.........9995[-2.5784128, 10.5256405, 23.895123, 8.827512, ...29996[-2.773907, 0.56169015, 1.6811254, 15.230703, ...39997[-5.575542, -2.2075167, -9.225033, -5.60418, 1...49998[0.5491407, -7.7017508, -5.8287773, 2.2394006,...59999[3.5516088, -8.265893, -0.59651583, -4.034732,...610000 rows × 2 columns
table[0].values array([array([ -1.8004757 , -0.17253768, 1.4764961 , 3.0824265 ,-2.545419 , -0.76911056, -12.368087 , 13.539932 ,-0.6261405 , 3.832048 ], dtype=float32) ,array([ 4.323273 , 7.601658 , 16.587166 , 3.6476722 , -6.6673512 ,-6.05786 , -1.5660243 , -0.05598306, 5.20656 , -7.0792093 ],dtype=float32) ,array([-2.1820781, 9.377863 , 0.7748679, -3.0049446, 1.3374403,-1.6612737, 0.8854448, 1.8749483, 1.6950815, -2.9421623],dtype=float32) ,...,array([-5.575542 , -2.2075167 , -9.225033 , -5.60418 , 17.216341 ,2.8671436 , 1.0113716 , -0.24509335, 3.3702612 , 1.2950805 ],dtype=float32) ,array([ 0.5491407, -7.7017508, -5.8287773, 2.2394006, -7.533697 ,13.003905 , 6.1807218, -7.6733685, 9.39456 , -1.9602803],dtype=float32) ,array([ 3.5516088 , -8.265893 , -0.59651583, -4.034732 , 1.3853229 ,6.1974382 , 16.321545 , -8.593432 , 1.0132635 , -2.2048213 ],dtype=float32) ],dtype=object) table["pred"]=[np.argmax(table[0][i]) for i in range(table.shape[0])]table 01pred0[-1.8004757, -0.17253768, 1.4764961, 3.0824265...771[4.323273, 7.601658, 16.587166, 3.6476722, -6....222[-2.1820781, 9.377863, 0.7748679, -3.0049446, ...113[13.455704, -9.902006, 2.8586285, -2.2104588, ...004[-2.9572597, -2.5707455, -3.5142026, -1.748683...44............9995[-2.5784128, 10.5256405, 23.895123, 8.827512, ...229996[-2.773907, 0.56169015, 1.6811254, 15.230703, ...339997[-5.575542, -2.2075167, -9.225033, -5.60418, 1...449998[0.5491407, -7.7017508, -5.8287773, 2.2394006,...559999[3.5516088, -8.265893, -0.59651583, -4.034732,...6610000 rows × 3 columns
13. 对预测错误的样本点进行可视化 mismatch=table[table[1]!=table["pred"]] mismatch 01pred247[-0.28747877, 1.9184055, 8.627771, -3.1354206,...42340[-5.550468, 1.6552217, -0.96347404, 9.110174, ...53449[-6.0154114, -3.7659, -2.7571707, 14.220249, -...35582[-1.4626387, 1.3258317, 10.138913, 5.996572, -...82659[-3.1300178, 8.830592, 8.781635, 5.6512327, -3...21............9768[2.6190603, -5.539648, 3.0145228, 4.8416886, -...239770[7.0385275, -9.72994, 0.03886398, -0.3356622, ...569792[-0.84618676, -0.038114145, -4.388391, 0.12577...499904[1.6193992, -7.525599, 2.833153, 3.7744582, -2...289982[0.8662107, -7.932593, -0.3750058, 1.9749051, ...56158 rows × 3 columns
from matplotlib import pyplot as pltplt.scatter(mismatch[1],mismatch["pred"]) <matplotlib.collections.PathCollection at 0x217dc403490> 14. 看看错误样本被预测为哪些数据 mismatch[mismatch[1]==8].sort_values("pred").index Int64Index([4807, 2896, 582, 6625, 7220, 3871, 4123, 1878, 1319, 2179, 4601,4956, 3023, 9280, 8408, 6765, 4497, 1530, 947],dtype='int64') table.iloc[4500,:] 0 [-4.9380565, 6.2523484, -1.2272537, 0.32682633...1 9pred 1Name: 4500, dtype: object idx_lst=mismatch[mismatch[1]==8].sort_values("pred").index.valuesidx_lst,len(idx_lst) (array([4807, 2896, 582, 6625, 7220, 3871, 4123, 1878, 1319, 2179, 4601,4956, 3023, 9280, 8408, 6765, 4497, 1530, 947], dtype=int64),19) mismatch[mismatch[1]==8].sort_values("pred") 01pred4807[5.3192024, -4.2546616, 3.6083155, 3.8956034, ...802896[7.4840407, -8.972937, 0.9461607, 1.6278361, -...80582[-1.4626387, 1.3258317, 10.138913, 5.996572, -...826625[-5.413072, 2.7984824, 6.0430045, 2.3938487, 0...827220[-3.1443837, -3.4629154, 4.8560658, 12.752452,...833871[0.1749076, -5.8143945, 3.083826, 8.113558, -5...834123[-3.8682778, -2.290763, 6.1067047, 10.920237, ...831878[-2.8437655, -2.4290323, 3.1861248, 9.739316, ...831319[3.583813, -6.279593, -0.21310738, 7.2746606, ...832179[-0.57300043, -3.8434098, 8.02766, 12.139142, ...834601[-9.5640745, -2.1305811, -5.2161045, 2.3105593...844956[-7.5286517, -4.080871, -6.850239, -2.9094412,...843023[-2.6319933, -11.065216, -1.3231966, 0.0415189...859280[-1.9706918, -11.544259, -0.51283014, 3.955923...858408[1.0573181, -3.7079592, 0.34973174, -0.3489528...866765[2.8831, -2.6855779, 0.39529848, -1.855415, -2...864497[-4.830113, -0.28656, 4.911254, 4.4041815, -2....871530[-4.4495664, -2.5381584, 5.4418654, 9.994939, ...87947[-2.8835857, -8.3713045, -1.5150836, 3.1263702...89 import numpy as npimg=np.stack(list(test_dataset[idx_lst[i]][0][0] for i in range(5)),axis=1).reshape(28,28*5)plt.imshow(img) <matplotlib.image.AxesImage at 0x217dc28e9d0> #显示3行import numpy as npimg30=np.stack(tuple(np.stack(tuple(test_dataset[idx_lst[i+j*5]][0][0] for i in range(5)),axis=1).reshape(28,28*5) for j in range(3)),axis=0).reshape(28*3,28*5)plt.imshow(img30)plt.axis('off') (-0.5, 139.5, 83.5, -0.5) arr2=table.iloc[idx_lst[:30],2].valuesarr2 array([0, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 9],dtype=int64)
