softmax分类器_一文看懂如何实现softmax分类器（内附完全代码）

#实现softmax回归
import torch
import torchvision
import sys
import numpy as npfrom IPython import display
from numpy import argmax
import torchvision.transforms as transforms
from time import time
import matplotlib.pyplot as plt

batch_size &＃61; 256mnist_train &＃61; torchvision.datasets.FashionMNIST(root&＃61;&＃39;~/Datasets/FashionMNIST&＃39;,train&＃61;True,download&＃61;True,transform&＃61;transforms.ToTensor())
#获取训练集
mnist_test &＃61; torchvision.datasets.FashionMNIST(root&＃61;&＃39;~/Datasets/FashionMNIST&＃39;,train&＃61;False,download&＃61;True,transform&＃61;transforms.ToTensor())
#获取测试集&＃xff08;这两个数据集在已存在的情况下不会被再次下载&＃xff09;#生成迭代器&＃xff08;调用一次返回一次数据&＃xff09;
train_iter &＃61; torch.utils.data.DataLoader(mnist_train,batch_size&＃61;batch_size,shuffle &＃61; True,num_workers &＃61; 0)test_iter &＃61; torch.utils.data.DataLoader(mnist_test,batch_size &＃61; batch_size,shuffle&＃61;False,num_workers&＃61;0)

num_inputs &＃61; 784
num_outputs &＃61; 10#初始化参数与线性回归也类似&＃xff0c;权重参数设置为均值为0 标准差为0.01的正态分布&＃xff1b;偏差设置为0
W &＃61; torch.tensor(np.random.normal(0,0.01,(num_inputs,num_outouts)),dtype &＃61; torch.float)
b &＃61; torch.zeros(num_outputs,dtype&＃61;torch.float32)#同样的&＃xff0c;开启模型参数梯度
W.requires_grad_(requires_grad&＃61;True)
b.requires_grad_(requires_grad&＃61;True)

X &＃61; torch.tensor([[1,2,3],[4,5,6]])#dim&＃61;0表示对列求和。keepdim表示是否在结果中保留行和列这两个维度
X.sum(dim&＃61;0,keepdim&＃61;True)
X.sum(dim&＃61;1,keepdim&＃61;True)

def softmax(X):X_exp &＃61; X.exp()partition &＃61; X_exp.sum(dim&＃61;1,keepdim&＃61;True)return X_exp/partition #这部分用了广播机制

def net(X):return softmax(torch.mm(X.view((-1,num_inputs)), W) &＃43;b)#第一步&＃xff1a;首先将X换形成28*28的张量&＃xff0c;然后用.mm函数将换形后的张量与权重参数相乘&＃xff0c;最后加偏差参数#第二步&＃xff1a;对第一步进行softmax运算

#gather函数的定义
torch.gather(input,dim,index,out&＃61;None) → Tensor
#gather的作用是这样的&＃xff0c;index实际上是索引&＃xff0c;具体是行&＃xff08;dim&＃61;1&＃xff09;还是列&＃xff08;dim&＃61;0&＃xff09;的索引要看前面dim 的指定&＃xff0c;输出的大小由index决定

假设输入与上同&＃xff1b;index&＃61;B&＃xff1b;输出为C
B中每个元素分别为b(0,0)&＃61;0,b(0,1)&＃61;0b(1,0)&＃61;1,b(1,1)&＃61;0如果dim&＃61;0&＃xff08;列&＃xff09;
则取B中元素的列号&＃xff0c;如&＃xff1a;b(0,1)的1
b(0,1)&＃61;0&＃xff0c;所以C中的c(0,1)&＃61;输入的(0,1)处元素2如果dim&＃61;1&＃xff08;行&＃xff09;
则取B中元素的列号&＃xff0c;如&＃xff1a;b(0,1)的0
b(0,1)&＃61;0&＃xff0c;所以C中的c(0,1)&＃61;输入的(0,0)处元素1总结如下&＃xff1a;
输出 元素 在 输入张量 中的位置为&＃xff1a;
输出元素位置取决与同位置的index元素
dim&＃61;1时&＃xff0c;取同位置的index元素的行号做行号&＃xff0c;该位置处index元素做列号
dim&＃61;0时&＃xff0c;取同位置的index元素的列号做列号&＃xff0c;该位置处index元素做行号。最后根据得到的索引在输入中取值index类型必须为LongTensor
gather最终的输出变量与index同形。

import torcha &＃61; torch.Tensor([[1,2],[3,4]])b &＃61; torch.gather(a,1,torch.LongTensor([[0,0],[1,0]]))
#1. 取各个元素行号&＃xff1a;[(0,y)(0,y)][(1,y)(1,y)]
#2. 取各个元素值做行号&＃xff1a;[(0,0)(0,0)][(1,1)(1,0)]
#3. 根据得到的索引在输入中取值
#[1,1],[4,3]c &＃61; torch.gather(a,0,torch.LongTensor([[0,0],[1,0]]))
#1. 取各个元素列号&＃xff1a;[(x,0)(x,1)][(x,0)(x,1)]
#2. 取各个元素值做行号&＃xff1a;[(0,0)(0,1)][(1,0)(0,1)]
#3. 根据得到的索引在输入中取值
#[1,2],[3,2]

y_hat &＃61; torch.tensor([0.1,0.3,0.6])
y &＃61; torch.LongTensor([0]) #gather函数中的index参数类型必须为LongTensor
y_hat.gather(1,y.vies(-1,1))
#如果y不是列向量&＃xff0c;则需要将变量y换形为列向量。选取第一维度&＃xff08;行&＃xff09;。
#套用上述公式可知&＃xff0c;输出为0.1&＃xff0c;0.1就是真是类别0的概率。

def cross_entropy(y_hat,y):return -torch.log(y_hat.gather(1,y.view(-1,1)))

我们把预测概率最大的类别作为输出类别&＃xff0c;如果它与真实类别y一致&＃xff0c;说明预测正确。分类准确率就是正确预测数量与总预测数量之比

#argmax(f(x))函数&＃xff0c;对f(x)求最大值所对应的点x。我们令f(x)&＃61; dim&＃61;1&＃xff0c;即可实现求所有行上的最大值对应的索引。
A &＃61; y_hat.argmax(dim&＃61;1)
#最终输出结果为一个行数与y_hat相同的列向量

B &＃61; (y_hat.argmax(dim&＃61;1)&＃61;&＃61;y).float()
#由于y_hat.argmax(dim&＃61;1)&＃61;&＃61;y得到的是ByteTensor型数据&＃xff0c;所以我们通过.float()将其转换为浮点型Tensor()

(y_hat.argmax(dim&＃61;1)&＃61;&＃61;y).float().mean()

(y_hat.argmax(dim&＃61;1)&＃61;&＃61;y).float().mean().item()
#pytorch number的获取统一通过.item()实现

def accuracy(y_hat,y):return (y_hat.argmax(dim&＃61;1).float().mean().item())

def net_accurary(data_iter,net):right_sum,n &＃61; 0.0,0for X,y in data_iter:#从迭代器data_iter中获取X和yright_sum &＃43;&＃61; (net(X).argmax(dim&＃61;1)&＃61;&＃61;y).float().sum().item()#计算准确判断的数量n &＃43;&＃61;y.shape[0]#通过shape[0]获取y的零维度&＃xff08;列&＃xff09;的元素数量return right_sum/n

def sgd(params,lr,batch_size):#lr&＃xff1a;学习率,params&＃xff1a;权重参数和偏差参数for param in params:param.data -&＃61; lr*param.grad/batch_size#.data是对数据备份进行操作&＃xff0c;不改变数据本身。

num_epochs,lr &＃61; 5,0.1def train_softmax(net,train_iter,test_iter,loss,num_epochs,batch_size,params,lr ,optimizer):for epoch in range(num_epochs):#损失值、正确数量、总数 初始化。train_l_sum,train_right_sum,n&＃61; 0.0,0.0,0for X,y in train_iter:y_hat &＃61; net(X)l &＃61; loss(y_hat,y).sum()#数据集损失函数的值&＃61;每个样本的损失函数值的和。 if optimizer is not None:optimizer.zero_grad() #对优化函数梯度清零elif params is not None and params[0].grad is not None:for param in params:param.grad.data.zero_()l.backgrad() #对损失函数求梯度optimzer(params,lr,batch_size)train_l_sum &＃43;&＃61; l.item()train_right_sum &＃43;&＃61; (y_hat.argmax(dim&＃61;1) &＃61;&＃61; y).sum().item()n &＃43;&＃61; y.shape[0]test_acc &＃61; net_accuracy(test_iter, net) #测试集的准确率print(&＃39;epoch %d, loss %.4f, train acc %.3f, test acc %.3f&＃39; % (epoch &＃43; 1, train_l_sum / n, train_acc_sum / n, test_acc))train_softmax(net,train_iter,test_iter,cross_entropy,num_epochs,batch_size,[W,b],lr,sgd)

def get_Fashion_MNIST_labels(labels):text_labels &＃61; [&＃39;t-shirt&＃39;, &＃39;trouser&＃39;, &＃39;pullover&＃39;, &＃39;dress&＃39;, &＃39;coat&＃39;,&＃39;sandal&＃39;, &＃39;shirt&＃39;, &＃39;sneaker&＃39;, &＃39;bag&＃39;, &＃39;ankle boot&＃39;]return [text_labels[int(i)] for i in labels]#labels是一个列表&＃xff0c;所以有了for循环获取这个列表对应的文本列表def show_fashion_mnist(images,labels):display.set_matplotlib_formats(&＃39;svg&＃39;)#绘制矢量图_,figs &＃61; plt.subplots(1,len(images),figsize&＃61;(12,12))#设置添加子图的数量、大小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 &＃61; iter(test_iter).next()true_labels &＃61; get_Fashion_MNIST_labels(y.numpy())
pred_labels &＃61; get_Fashion_MNIST_labels(net(X).argmax(dim&＃61;1).numpy())
titles &＃61; [true &＃43; &＃39;n&＃39; &＃43; pred for true, pred in zip(true_labels, pred_labels)]show_fashion_mnist(X[0:9], titles[0:9])

#实现softmax回归
import torch
import torchvision
import sys
import numpy as npfrom IPython import display
from numpy import argmax
import torchvision.transforms as transforms
from time import time
import matplotlib.pyplot as pltbatch_size &＃61;256
num_inputs &＃61; 784
num_outputs &＃61; 10
num_epochs,lr &＃61; 5,0.1mnist_train &＃61; torchvision.datasets.FashionMNIST(root&＃61;&＃39;~/Datasets/FashionMNIST&＃39;,train&＃61;True,download&＃61;True,transform&＃61;transforms.ToTensor())
#获取训练集
mnist_test &＃61; torchvision.datasets.FashionMNIST(root&＃61;&＃39;~/Datasets/FashionMNIST&＃39;,train&＃61;False,download&＃61;True,transform&＃61;transforms.ToTensor())
#获取测试集&＃xff08;这两个数据集在已存在的情况下不会被再次下载&＃xff09;#生成迭代器&＃xff08;调用一次返回一次数据&＃xff09;
train_iter &＃61; torch.utils.data.DataLoader(mnist_train,batch_size&＃61;batch_size,shuffle &＃61; True,num_workers &＃61; 0)test_iter &＃61; torch.utils.data.DataLoader(mnist_test,batch_size &＃61; batch_size,shuffle&＃61;False,num_workers&＃61;0)#初始化参数与线性回归也类似&＃xff0c;权重参数设置为均值为0 标准差为0.01的正态分布&＃xff1b;偏差设置为0
W &＃61; torch.tensor(np.random.normal(0,0.01,(num_inputs,num_outputs)),dtype &＃61; torch.float)
b &＃61; torch.zeros(num_outputs,dtype&＃61;torch.float32)#同样的&＃xff0c;开启模型参数梯度
W.requires_grad_(requires_grad&＃61;True)
b.requires_grad_(requires_grad&＃61;True)def softmax(X):X_exp &＃61; X.exp()partition &＃61; X_exp.sum(dim&＃61;1,keepdim&＃61;True)return X_exp/partition #这部分用了广播机制def net(X):return softmax(torch.mm(X.view((-1,num_inputs)), W) &＃43;b)def cross_entropy(y_hat,y):return -torch.log(y_hat.gather(1,y.view(-1,1)))def accuracy(y_hat,y):return (y_hat.argmax(dim&＃61;1).float().mean().item())def net_accurary(data_iter,net):right_sum,n &＃61; 0.0,0for X,y in data_iter:#从迭代器data_iter中获取X和yright_sum &＃43;&＃61; (net(X).argmax(dim&＃61;1)&＃61;&＃61;y).float().sum().item()#计算准确判断的数量n &＃43;&＃61;y.shape[0]#通过shape[0]获取y的零维度&＃xff08;列&＃xff09;的元素数量return right_sum/ndef sgd(params,lr,batch_size):#lr&＃xff1a;学习率,params&＃xff1a;权重参数和偏差参数for param in params:param.data -&＃61; lr*param.grad/batch_sizedef train_softmax(net,train_iter,test_iter,loss,num_epochs,batch_size,params,lr ,optimizer,net_accuracy):for epoch in range(num_epochs):#损失值、正确数量、总数 初始化。train_l_sum,train_right_sum,n&＃61; 0.0,0.0,0for X,y in train_iter:y_hat &＃61; net(X)l &＃61; loss(y_hat,y).sum()#数据集损失函数的值&＃61;每个样本的损失函数值的和。 if params is not None and params[0].grad is not None:for param in params:param.grad.data.zero_()l.backward() #对损失函数求梯度optimizer(params,lr,batch_size)train_l_sum &＃43;&＃61; l.item()train_right_sum &＃43;&＃61; (y_hat.argmax(dim&＃61;1) &＃61;&＃61; y).sum().item()n &＃43;&＃61; y.shape[0]test_acc &＃61; net_accurary(test_iter, net) #测试集的准确率print(&＃39;epoch %d, loss %.4f, train right %.3f, test right %.3f&＃39; % (epoch &＃43; 1, train_l_sum / n, train_right_sum / n, test_acc))def get_Fashion_MNIST_labels(labels):text_labels &＃61; [&＃39;t-shirt&＃39;, &＃39;trouser&＃39;, &＃39;pullover&＃39;, &＃39;dress&＃39;, &＃39;coat&＃39;,&＃39;sandal&＃39;, &＃39;shirt&＃39;, &＃39;sneaker&＃39;, &＃39;bag&＃39;, &＃39;ankle boot&＃39;]return [text_labels[int(i)] for i in labels]#labels是一个列表&＃xff0c;所以有了for循环获取这个列表对应的文本列表def show_fashion_mnist(images,labels):display.set_matplotlib_formats(&＃39;svg&＃39;)#绘制矢量图_,figs &＃61; plt.subplots(1,len(images),figsize&＃61;(12,12))#设置添加子图的数量、大小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()time1 &＃61; time()
train_softmax(net,train_iter,test_iter,cross_entropy,num_epochs,batch_size,[W,b],lr,sgd,net_accurary)
print(&＃39;n&＃39;,time()-time1,&＃39;s&＃39;)X, y &＃61; iter(test_iter).next()true_labels &＃61; get_Fashion_MNIST_labels(y.numpy())
pred_labels &＃61; get_Fashion_MNIST_labels(net(X).argmax(dim&＃61;1).numpy())
titles &＃61; [true &＃43; &＃39;n&＃39; &＃43; pred for true, pred in zip(true_labels, pred_labels)]show_fashion_mnist(X[0:9], titles[0:9])