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這篇文章將為大家詳細(xì)講解有關(guān)PyTorch: Softmax多分類是什么,小編覺得挺實(shí)用的,因此分享給大家做個(gè)參考,希望大家閱讀完這篇文章后可以有所收獲。
多分類一種比較常用的做法是在最后一層加softmax歸一化,值最大的維度所對(duì)應(yīng)的位置則作為該樣本對(duì)應(yīng)的類。本文采用PyTorch框架,選用經(jīng)典圖像數(shù)據(jù)集mnist學(xué)習(xí)一波多分類。
MNIST數(shù)據(jù)集
MNIST 數(shù)據(jù)集(手寫數(shù)字?jǐn)?shù)據(jù)集)來自美國(guó)國(guó)家標(biāo)準(zhǔn)與技術(shù)研究所, National Institute of Standards and Technology (NIST). 訓(xùn)練集 (training set) 由來自 250 個(gè)不同人手寫的數(shù)字構(gòu)成, 其中 50% 是高中學(xué)生, 50% 來自人口普查局 (the Census Bureau) 的工作人員. 測(cè)試集(test set) 也是同樣比例的手寫數(shù)字?jǐn)?shù)據(jù)。MNIST數(shù)據(jù)集下載地址:http://yann.lecun.com/exdb/mnist/。手寫數(shù)字的MNIST數(shù)據(jù)庫(kù)包括60,000個(gè)的訓(xùn)練集樣本,以及10,000個(gè)測(cè)試集樣本。
其中:
train-images-idx3-ubyte.gz (訓(xùn)練數(shù)據(jù)集圖片)
train-labels-idx1-ubyte.gz (訓(xùn)練數(shù)據(jù)集標(biāo)記類別)
t10k-images-idx3-ubyte.gz: (測(cè)試數(shù)據(jù)集)
t10k-labels-idx1-ubyte.gz(測(cè)試數(shù)據(jù)集標(biāo)記類別)
MNIST數(shù)據(jù)集是經(jīng)典圖像數(shù)據(jù)集,包括10個(gè)類別(0到9)。每一張圖片拉成向量表示,如下圖784維向量作為第一層輸入特征。
Softmax分類
softmax函數(shù)的本質(zhì)就是將一個(gè)K 維的任意實(shí)數(shù)向量壓縮(映射)成另一個(gè)K維的實(shí)數(shù)向量,其中向量中的每個(gè)元素取值都介于(0,1)之間,并且壓縮后的K個(gè)值相加等于1(變成了概率分布)。在選用Softmax做多分類時(shí),可以根據(jù)值的大小來進(jìn)行多分類的任務(wù),如取權(quán)重最大的一維。softmax介紹和公式網(wǎng)上很多,這里不介紹了。下面使用Pytorch定義一個(gè)多層網(wǎng)絡(luò)(4個(gè)隱藏層,最后一層softmax概率歸一化),輸出層為10正好對(duì)應(yīng)10類。
PyTorch實(shí)戰(zhàn)
import torch import torch.nn as nn import torch.nn.functional as F import torch.optim as optim from torchvision import datasets, transforms from torch.autograd import Variable # Training settings batch_size = 64 # MNIST Dataset train_dataset = datasets.MNIST(root='./mnist_data/', train=True, transform=transforms.ToTensor(), download=True) test_dataset = datasets.MNIST(root='./mnist_data/', train=False, transform=transforms.ToTensor()) # Data Loader (Input Pipeline) train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True) test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=batch_size, shuffle=False) class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.l1 = nn.Linear(784, 520) self.l2 = nn.Linear(520, 320) self.l3 = nn.Linear(320, 240) self.l4 = nn.Linear(240, 120) self.l5 = nn.Linear(120, 10) def forward(self, x): # Flatten the data (n, 1, 28, 28) --> (n, 784) x = x.view(-1, 784) x = F.relu(self.l1(x)) x = F.relu(self.l2(x)) x = F.relu(self.l3(x)) x = F.relu(self.l4(x)) return F.log_softmax(self.l5(x), dim=1) #return self.l5(x) model = Net() optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5) def train(epoch): # 每次輸入barch_idx個(gè)數(shù)據(jù) for batch_idx, (data, target) in enumerate(train_loader): data, target = Variable(data), Variable(target) optimizer.zero_grad() output = model(data) # loss loss = F.nll_loss(output, target) loss.backward() # update optimizer.step() if batch_idx % 200 == 0: print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format( epoch, batch_idx * len(data), len(train_loader.dataset), 100. * batch_idx / len(train_loader), loss.data[0])) def test(): test_loss = 0 correct = 0 # 測(cè)試集 for data, target in test_loader: data, target = Variable(data, volatile=True), Variable(target) output = model(data) # sum up batch loss test_loss += F.nll_loss(output, target).data[0] # get the index of the max pred = output.data.max(1, keepdim=True)[1] correct += pred.eq(target.data.view_as(pred)).cpu().sum() test_loss /= len(test_loader.dataset) print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format( test_loss, correct, len(test_loader.dataset), 100. * correct / len(test_loader.dataset))) for epoch in range(1,6): train(epoch) test() 輸出結(jié)果: Train Epoch: 1 [0/60000 (0%)] Loss: 2.292192 Train Epoch: 1 [12800/60000 (21%)] Loss: 2.289466 Train Epoch: 1 [25600/60000 (43%)] Loss: 2.294221 Train Epoch: 1 [38400/60000 (64%)] Loss: 2.169656 Train Epoch: 1 [51200/60000 (85%)] Loss: 1.561276 Test set: Average loss: 0.0163, Accuracy: 6698/10000 (67%) Train Epoch: 2 [0/60000 (0%)] Loss: 0.993218 Train Epoch: 2 [12800/60000 (21%)] Loss: 0.859608 Train Epoch: 2 [25600/60000 (43%)] Loss: 0.499748 Train Epoch: 2 [38400/60000 (64%)] Loss: 0.422055 Train Epoch: 2 [51200/60000 (85%)] Loss: 0.413933 Test set: Average loss: 0.0065, Accuracy: 8797/10000 (88%) Train Epoch: 3 [0/60000 (0%)] Loss: 0.465154 Train Epoch: 3 [12800/60000 (21%)] Loss: 0.321842 Train Epoch: 3 [25600/60000 (43%)] Loss: 0.187147 Train Epoch: 3 [38400/60000 (64%)] Loss: 0.469552 Train Epoch: 3 [51200/60000 (85%)] Loss: 0.270332 Test set: Average loss: 0.0045, Accuracy: 9137/10000 (91%) Train Epoch: 4 [0/60000 (0%)] Loss: 0.197497 Train Epoch: 4 [12800/60000 (21%)] Loss: 0.234830 Train Epoch: 4 [25600/60000 (43%)] Loss: 0.260302 Train Epoch: 4 [38400/60000 (64%)] Loss: 0.219375 Train Epoch: 4 [51200/60000 (85%)] Loss: 0.292754 Test set: Average loss: 0.0037, Accuracy: 9277/10000 (93%) Train Epoch: 5 [0/60000 (0%)] Loss: 0.183354 Train Epoch: 5 [12800/60000 (21%)] Loss: 0.207930 Train Epoch: 5 [25600/60000 (43%)] Loss: 0.138435 Train Epoch: 5 [38400/60000 (64%)] Loss: 0.120214 Train Epoch: 5 [51200/60000 (85%)] Loss: 0.266199 Test set: Average loss: 0.0026, Accuracy: 9506/10000 (95%) Process finished with exit code 0
隨著訓(xùn)練迭代次數(shù)的增加,測(cè)試集的精確度還是有很大提高的。并且當(dāng)?shù)螖?shù)為5時(shí),使用這種簡(jiǎn)單的網(wǎng)絡(luò)可以達(dá)到95%的精確度。
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