基于Pytorch實(shí)現(xiàn)分類器的示例詳解

更新時(shí)間：2023年04月17日 15:14:29 作者：N3ptune

這篇文章主要為大家詳細(xì)介紹了如何基于Pytorch實(shí)現(xiàn)兩個(gè)分類器:?softmax分類器和感知機(jī)分類器，文中的示例代碼講解詳細(xì)，需要的可以參考一下

Softmax分類器

Softmax分類是一種常用的多類別分類算法，它可以將輸入數(shù)據(jù)映射到一個(gè)概率分布上。Softmax分類首先將輸入數(shù)據(jù)通過線性變換得到一個(gè)向量，然后將向量中的每個(gè)元素進(jìn)行指數(shù)函數(shù)運(yùn)算，最后將指數(shù)運(yùn)算結(jié)果歸一化得到一個(gè)概率分布。這個(gè)概率分布可以被解釋為每個(gè)類別的概率估計(jì)。

定義

定義一個(gè)softmax分類器類:

class SoftmaxClassifier(nn.Module):
    def __init__(self,input_size,output_size):
        # 調(diào)用父類的__init__()方法進(jìn)行初始化
        super(SoftmaxClassifier,self).__init__()
        # 定義一個(gè)nn.Linear對象，用于將輸入特征映射到輸出類別
        self.linear = nn.Linear(input_size,output_size)
 
    def forward(self,x):
        x = self.linear(x) # 傳遞給線性層
        return nn.functional.softmax(x,dim=1) # 得到概率分布
 
    def compute_accuracy(self,output,labels):
        preds = torch.argmax(output,dim=1) # 獲取每個(gè)樣本的預(yù)測標(biāo)簽
        correct = torch.sum(preds == labels).item() # 計(jì)算正確預(yù)測的數(shù)量
        accuracy = correct / len(labels) # 除以總樣本數(shù)得到準(zhǔn)確率
        return accuracy

如上定義三個(gè)方法：

__init__(self)：構(gòu)造函數(shù)，在類初始化時(shí)運(yùn)行，調(diào)用父類的__init__()方法進(jìn)行初始化
forward(self)：模型前向計(jì)算過程
compute_accuracy(self)：計(jì)算模型的預(yù)測準(zhǔn)確率

訓(xùn)練

生成訓(xùn)練數(shù)據(jù):

import numpy as np
 
# 生成隨機(jī)樣本(包含訓(xùn)練數(shù)據(jù)和測試數(shù)據(jù))
def generate_rand_samples(dot_num=100):
    x_p = np.random.normal(3., 1, dot_num)
    y_p = np.random.normal(3., 1, dot_num)
    y = np.zeros(dot_num)
    C1 = np.array([x_p, y_p, y]).T
    x_n = np.random.normal(7., 1, dot_num)
    y_n = np.random.normal(7., 1, dot_num)
    y = np.ones(dot_num)
    C2 = np.array([x_n, y_n, y]).T
    x_n = np.random.normal(3., 1, dot_num)
    y_n = np.random.normal(7., 1, dot_num)
    y = np.ones(dot_num)*2
    C3 = np.array([x_n, y_n, y]).T
    x_n = np.random.normal(7, 1, dot_num)
    y_n = np.random.normal(3, 1, dot_num)
    y = np.ones(dot_num)*3
    C4 = np.array([x_n, y_n, y]).T
    data_set = np.concatenate((C1, C2, C3, C4), axis=0)
    np.random.shuffle(data_set)
 
    return data_set[:,:2].astype(np.float32),data_set[:,2].astype(np.int32)
 
X_train,y_train = generate_rand_samples()
y_train[y_train == -1] = 0

設(shè)置訓(xùn)練前的前置參數(shù)，并初始化分類器

num_inputs = 2  # 輸入維度大小
num_outputs = 4  # 輸出維度大小
learning_rate = 0.01  # 學(xué)習(xí)率
num_epochs = 2000 # 訓(xùn)練周期數(shù)
 
# 歸一化數(shù)據(jù) 將數(shù)據(jù)特征減去均值再除以標(biāo)準(zhǔn)差
X_train = (X_train - X_train.mean(axis=0)) / X_train.std(axis=0)
y_train = y_train.astype(np.compat.long)
 
# 創(chuàng)建model并初始化
model = SoftmaxClassifier(num_inputs, num_outputs)
criterion = nn.CrossEntropyLoss() # 交叉熵?fù)p失
optimizer = optim.SGD(model.parameters(), lr=learning_rate)  # SGD優(yōu)化器

訓(xùn)練:

# 遍歷訓(xùn)練周期數(shù)
for epoch in range(num_epochs):
    outputs = model(torch.tensor(X_train))  # 前向傳遞計(jì)算
    loss = criterion(outputs,torch.tensor(y_train))  # 計(jì)算預(yù)測輸出和真實(shí)標(biāo)簽之間的損失
    train_accuracy = model.compute_accuracy(outputs,torch.tensor(y_train))  # 計(jì)算模型當(dāng)前訓(xùn)練周期中準(zhǔn)確率
 
    optimizer.zero_grad()  # 清楚優(yōu)化器中梯度
    loss.backward()  # 計(jì)算損失對模型參數(shù)的梯度
    optimizer.step()
    
    # 打印信息
    if (epoch + 1) % 10 == 0:
        print(f"Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}, Accuracy: {train_accuracy:.4f}")

運(yùn)行：

Epoch [1820/2000], Loss: 0.9947, Accuracy: 0.9575
Epoch [1830/2000], Loss: 0.9940, Accuracy: 0.9600
Epoch [1840/2000], Loss: 0.9932, Accuracy: 0.9600
Epoch [1850/2000], Loss: 0.9925, Accuracy: 0.9600
Epoch [1860/2000], Loss: 0.9917, Accuracy: 0.9600
....

測試

生成測試并測試:

X_test, y_test = generate_rand_samples()  # 生成測試數(shù)據(jù)
X_test = (X_test- np.mean(X_test)) / np.std(X_test)  # 歸一化
y_test = y_test.astype(np.compat.long)
predicts = model(torch.tensor(X_test))  # 獲取模型輸出
accuracy = model.compute_accuracy(predicts,torch.tensor(y_test))  # 計(jì)算準(zhǔn)確度
print(f'Test Accuracy: {accuracy:.4f}')

輸出：

Test Accuracy: 0.9725

繪制圖像:

# 繪制圖像
x_min, x_max = X_test[:, 0].min() - 1, X_test[:, 0].max() + 1
y_min, y_max = X_test[:, 1].min() - 1, X_test[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1))
Z = model(torch.tensor(np.c_[xx.ravel(), yy.ravel()], dtype=torch.float32)).argmax(dim=1).numpy()
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, alpha=0.4)
plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test, s=20, edgecolor='k')
plt.show()

感知機(jī)分類器

實(shí)現(xiàn)與上述softmax分類器相似，此處實(shí)現(xiàn)sigmod感知機(jī)，采用sigmod作為分類函數(shù)，該函數(shù)可以將線性變換的結(jié)果映射為0到1之間的實(shí)數(shù)值，通常被用作神經(jīng)網(wǎng)絡(luò)中的激活函數(shù)

sigmoid感知機(jī)的學(xué)習(xí)算法與普通的感知機(jī)類似，也是采用隨機(jī)梯度下降（SGD）的方式進(jìn)行更新。不同之處在于，sigmoid感知機(jī)的輸出是一個(gè)概率值，需要將其轉(zhuǎn)化為類別標(biāo)簽。

通常使用閾值來決定輸出值所屬的類別，如將輸出值大于0.5的樣本歸為正類，小于等于0.5的樣本歸為負(fù)類。

定義

# 感知機(jī)分類器
class PerceptronClassifier(nn.Module):
    def __init__(self, input_size,output_size):
        super(PerceptronClassifier, self).__init__()
        self.linear = nn.Linear(input_size,output_size)
 
    def forward(self, x):
        logits = self.linear(x)
        return torch.sigmoid(logits)
 
    def compute_accuracy(self, pred, target):
        pred = torch.where(pred >= 0.5, 1, -1)
        accuracy = (pred == target).sum().item() / target.size(0)
        return accuracy

給定一個(gè)輸入向量(x1,x2,x3...xn)，輸出為y=σ(w⋅x+b)=1/(e^−(w⋅x+b))

訓(xùn)練

生成訓(xùn)練集:

def generate_rand_samples(dot_num=100):
    x_p = np.random.normal(3., 1, dot_num)
    y_p = np.random.normal(3., 1, dot_num)
    y = np.ones(dot_num)
    C1 = np.array([x_p, y_p, y]).T
    x_n = np.random.normal(6., 1, dot_num)
    y_n = np.random.normal(0., 1, dot_num)
    y = np.ones(dot_num)*-1
    C2 = np.array([x_n, y_n, y]).T
    data_set = np.concatenate((C1, C2), axis=0)
    np.random.shuffle(data_set)
    return data_set[:,:2].astype(np.float32),data_set[:,2].astype(np.int32)
 
X_train,y_train = generate_rand_samples()
X_test,y_test = generate_rand_samples()

該過程與上述softmax分類器相似:

num_inputs = 2
num_outputs = 1
learning_rate = 0.01
num_epochs = 200
 
# 歸一化數(shù)據(jù) 將數(shù)據(jù)特征減去均值再除以標(biāo)準(zhǔn)差
X_train = (X_train - X_train.mean(axis=0)) / X_train.std(axis=0)
 
# 創(chuàng)建model并初始化
model = PerceptronClassifier(num_inputs, num_outputs)
optimizer = optim.SGD(model.parameters(), lr=learning_rate)  # SGD優(yōu)化器
 
criterion = nn.functional.binary_cross_entropy

訓(xùn)練：

# 遍歷訓(xùn)練周期數(shù)
for epoch in range(num_epochs):
    outputs = model(torch.tensor(X_train))
    labels = torch.tensor(y_train).unsqueeze(1)
    loss = criterion(outputs,labels.float())
    train_accuracy = model.compute_accuracy(outputs, labels)
 
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
 
    if (epoch + 1) % 10 == 0:
        print(f"Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}, Accuracy: {train_accuracy:.4f}")

輸出:

Epoch [80/200], Loss: -0.5429, Accuracy: 0.9550
Epoch [90/200], Loss: -0.6235, Accuracy: 0.9550
Epoch [100/200], Loss: -0.7015, Accuracy: 0.9500
Epoch [110/200], Loss: -0.7773, Accuracy: 0.9400
....

測試

X_test, y_test = generate_rand_samples() # 生成測試集
X_test = (X_test - X_test.mean(axis=0)) / X_test.std(axis=0)
 
test_inputs = torch.tensor(X_test)
test_labels = torch.tensor(y_test).unsqueeze(1)
with torch.no_grad():
    outputs = model(test_inputs)
    accuracy = model.compute_accuracy(outputs, test_labels)
    print(f"Test Accuracy: {accuracy:.4f}")

繪圖:

x_min, x_max = X_test[:, 0].min() - 1, X_test[:, 0].max() + 1
y_min, y_max = X_test[:, 1].min() - 1, X_test[:, 1].max() + 1
xx, yy = torch.meshgrid(torch.linspace(x_min, x_max, 100), torch.linspace(y_min, y_max, 100))
 
# 預(yù)測每個(gè)點(diǎn)的類別
Z = torch.argmax(model(torch.cat((xx.reshape(-1,1), yy.reshape(-1,1)), 1)), 1)
Z = Z.reshape(xx.shape)
 
# 繪制分類圖
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral,alpha=0.0)
 
# 繪制分界線
w = model.linear.weight.detach().numpy()  # 權(quán)重
b = model.linear.bias.detach().numpy()  # 偏置
x1 = np.linspace(x_min, x_max, 100)
x2 = (-b - w[0][0]*x1) / w[0][1]
plt.plot(x1, x2, 'k-')
 
# 繪制樣本點(diǎn)
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=plt.cm.Spectral)
plt.show()