softmax pytorch从零实现的代码

获取Fashion-MNIST训练集和读取数据

在介绍softmax回归的实现前我们先引入一个多类图像分类数据集。它将在后面的章节中被多次使用,以方便我们观察比较算法之间在模型精度和计算效率上的区别。图像分类数据集中最常用的是手写数字识别数据集MNIST[1]。但大部分模型在MNIST上的分类精度都超过了95%。为了更直观地观察算法之间的差异,我们将使用一个图像内容更加复杂的数据集Fashion-MNIST[2]。

我这里我们会使用torchvision包,它是服务于PyTorch深度学习框架的,主要用来构建计算机视觉模型。torchvision主要由以下几部分构成:

  1. torchvision.datasets: 一些加载数据的函数及常用的数据集接口;
  2. torchvision.models: 包含常用的模型结构(含预训练模型),例如AlexNet、VGG、ResNet等;
  3. torchvision.transforms: 常用的图片变换,例如裁剪、旋转等;
  4. torchvision.utils: 其他的一些有用的方法。


# import needed package
%matplotlib inline
from IPython import display
import matplotlib.pyplot as plt

import torch
import torchvision
import torchvision.transforms as transforms
import time

import sys
sys.path.append("/home/kesci/input")
import d2lzh1981 as d2l

print(torch.__version__)
print(torchvision.__version__)

get dataset

mnist_train = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=False, download=True, transform=transforms.ToTensor())

class torchvision.datasets.FashionMNIST(root, train=True, transform=None, target_transform=None, download=False)

  • root(string)– 数据集的根目录,其中存放processed/training.pt和processed/test.pt文件。
  • train(bool, 可选)– 如果设置为True,从training.pt创建数据集,否则从test.pt创建。
  • download(bool, 可选)– 如果设置为True,从互联网下载数据并放到root文件夹下。如果root目录下已经存在数据,不会再次下载。
  • transform(可被调用 , 可选)– 一种函数或变换,输入PIL图片,返回变换之后的数据。如:transforms.RandomCrop。
  • target_transform(可被调用 , 可选)– 一种函数或变换,输入目标,进行变换。
# show result 
print(type(mnist_train))
print(len(mnist_train), len(mnist_test))

# 我们可以通过下标来访问任意一个样本
feature, label = mnist_train[0]
print(feature.shape, label)  # Channel x Height x Width

如果不做变换输入的数据是图像,我们可以看一下图片的类型参数:

mnist_PIL = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True)
PIL_feature, label = mnist_PIL[0]
print(PIL_feature)
# 本函数已保存在d2lzh包中方便以后使用
def get_fashion_mnist_labels(labels):
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]# 读取数据
batch_size = 256
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)
def show_fashion_mnist(images, labels):
    d2l.use_svg_display()
    # 这里的_表示我们忽略(不使用)的变量
    _, figs = plt.subplots(1, len(images), figsize=(12, 12))
    for f, img, lbl in zip(figs, images, labels):
        f.imshow(img.view((28, 28)).numpy())
        f.set_title(lbl)
        f.axes.get_xaxis().set_visible(False)
        f.axes.get_yaxis().set_visible(False)
    plt.show()
X, y = [], []
for i in range(10):
    X.append(mnist_train[i][0]) # 将第i个feature加到X中
    y.append(mnist_train[i][1]) # 将第i个label加到y中
show_fashion_mnist(X, get_fashion_mnist_labels(y))
# 读取数据
batch_size = 256
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)

start = time.time()
for X, y in train_iter:
    continue
print('%.2f sec' % (time.time() - start))


softmax从零开始的实现

import torch
import torchvision
import numpy as np
import sys
sys.path.append("/home/kesci/input")
import d2lzh1981 as d2l

# 查看版本
print(torch.__version__)
print(torchvision.__version__)  

获取训练集数据和测试集数据

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, root='/home/kesci/input/FashionMNIST2065')

模型参数初始化

num_inputs = 784
print(28*28)
num_outputs = 10

W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)
b = torch.zeros(num_outputs, dtype=torch.float)

对多维Tensor按维度操作

X = torch.tensor([[1, 2, 3], [4, 5, 6]])
print(X.sum(dim=0, keepdim=True))  # dim为0,按照相同的列求和,并在结果中保留列特征
print(X.sum(dim=1, keepdim=True))  # dim为1,按照相同的行求和,并在结果中保留行特征
print(X.sum(dim=0, keepdim=False)) # dim为0,按照相同的列求和,不在结果中保留列特征
print(X.sum(dim=1, keepdim=False)) # dim为1,按照相同的行求和,不在结果中保留行特征

定义softmax操作

y ^ j = exp ⁡ ( o j ) ∑ i = 1 3 exp ⁡ ( o i ) \hat{y}_j = \frac{ \exp(o_j)}{\sum_{i=1}^3 \exp(o_i)} y^j=i=13exp(oi)exp(oj)

def softmax(X):
    X_exp = X.exp()
    partition = X_exp.sum(dim=1, keepdim=True)
    # print("X size is ", X_exp.size())
    # print("partition size is ", partition, partition.size())
    return X_exp / partition  # 这里应用了广播机制
   X = torch.rand((2, 5))
X_prob = softmax(X)
print(X_prob, '\n', X_prob.sum(dim=1))

softmax回归模型

o ( i ) = x ( i ) W + b , y ^ ( i ) = softmax ( o ( i ) ) . \begin{aligned} \boldsymbol{o}^{(i)} &= \boldsymbol{x}^{(i)} \boldsymbol{W} + \boldsymbol{b},\\ \boldsymbol{\hat{y}}^{(i)} &= \text{softmax}(\boldsymbol{o}^{(i)}). \end{aligned} o(i)y^(i)=x(i)W+b,=softmax(o(i)).

def net(X):
    return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)

定义损失函数

H ( y ( i ) , y ^ ( i ) ) = − ∑ j = 1 q y j ( i ) log ⁡ y ^ j ( i ) , H\left(\boldsymbol y^{(i)}, \boldsymbol {\hat y}^{(i)}\right ) = -\sum_{j=1}^q y_j^{(i)} \log \hat y_j^{(i)}, H(y(i),y^(i))=j=1qyj(i)logy^j(i),

ℓ ( Θ ) = 1 n ∑ i = 1 n H ( y ( i ) , y ^ ( i ) ) , \ell(\boldsymbol{\Theta}) = \frac{1}{n} \sum_{i=1}^n H\left(\boldsymbol y^{(i)}, \boldsymbol {\hat y}^{(i)}\right ), (Θ)=n1i=1nH(y(i),y^(i)),

ℓ ( Θ ) = − ( 1 / n ) ∑ i = 1 n log ⁡ y ^ y ( i ) ( i ) \ell(\boldsymbol{\Theta}) = -(1/n) \sum_{i=1}^n \log \hat y_{y^{(i)}}^{(i)} (Θ)=(1/n)i=1nlogy^y(i)(i)

y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
y = torch.LongTensor([0, 2])
y_hat.gather(1, y.view(-1, 1))
def cross_entropy(y_hat, y):
    return - torch.log(y_hat.gather(1, y.view(-1, 1))) 

定义准确率

def accuracy(y_hat, y):
    return (y_hat.argmax(dim=1) == y).float().mean().item()
print(accuracy(y_hat, y))
## 本函数已保存在d2lzh_pytorch包中方便以后使用。该函数将被逐步改进:它的完整实现将在“图像增广”一节中描述
def evaluate_accuracy(data_iter, net):
    acc_sum, n = 0.0, 0
    for X, y in data_iter:
        acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
        n += y.shape[0]
    return acc_sum / n
print(evaluate_accuracy(test_iter, net))

训练模型

num_epochs, lr = 5, 0.1
# 本函数已保存在d2lzh_pytorch包中方便以后使用
def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,
              params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
        for X, y in train_iter:
            y_hat = net(X)
            l = loss(y_hat, y).sum()
            
            # 梯度清零
            if optimizer is not None:
                optimizer.zero_grad()
            elif params is not None and params[0].grad is not None:
                for param in params:
                    param.grad.data.zero_()
            
            l.backward()
            if optimizer is None:
                d2l.sgd(params, lr, batch_size)
            else:
                optimizer.step() 
            
            
            train_l_sum += l.item()
            train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
            n += y.shape[0]
        test_acc = evaluate_accuracy(test_iter, net)
        print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'
              % (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))

train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)

模型预测

现在我们的模型训练完了,可以进行一下预测,我们的这个模型训练的到底准确不准确。
现在就可以演示如何对图像进行分类了。给定一系列图像(第三行图像输出),我们比较一下它们的真实标签(第一行文本输出)和模型预测结果(第二行文本输出)。

X, y = iter(test_iter).next()

true_labels = d2l.get_fashion_mnist_labels(y.numpy())
pred_labels = d2l.get_fashion_mnist_labels(net(X).argmax(dim=1).numpy())
titles = [true + '\n' + pred for true, pred in zip(true_labels, pred_labels)]

d2l.show_fashion_mnist(X[0:9], titles[0:9])

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