Pytorch實現分類器

本文實現兩個分類器: softmax分類器和感知機分類器

Softmax分類器

Softmax分類是一種常用的多類別分類演演算法，它可以將輸入資料對映到一個概率分佈上。Softmax分類首先將輸入資料通過線性變換得到一個向量，然後將向量中的每個元素進行指數函數運算，最後將指數運算結果歸一化得到一個概率分佈。這個概率分佈可以被解釋為每個類別的概率估計。

定義

定義一個softmax分類器類:

class SoftmaxClassifier(nn.Module):
    def __init__(self,input_size,output_size):
        # 呼叫父類別的__init__()方法進行初始化
        super(SoftmaxClassifier,self).__init__()
        # 定義一個nn.Linear物件，用於將輸入特徵對映到輸出類別
        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) # 得到概率分佈

    def compute_accuracy(self,output,labels):
        preds = torch.argmax(output,dim=1) # 獲取每個樣本的預測標籤
        correct = torch.sum(preds == labels).item() # 計算正確預測的數量
        accuracy = correct / len(labels) # 除以總樣本數得到準確率
        return accuracy

如上定義三個方法：

1. __init__(self)：建構函式，在類初始化時執行，呼叫父類別的__init__()方法進行初始化
2. forward(self)：模型前向計算過程
3. compute_accuracy(self)：計算模型的預測準確率

訓練

生成訓練資料:

import numpy as np

# 生成隨機樣本(包含訓練資料和測試資料)
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

設定訓練前的前置引數，並初始化分類器

num_inputs = 2  # 輸入維度大小
num_outputs = 4  # 輸出維度大小
learning_rate = 0.01  # 學習率
num_epochs = 2000 # 訓練週期數

# 歸一化資料 將資料特徵減去均值再除以標準差
X_train = (X_train - X_train.mean(axis=0)) / X_train.std(axis=0)
y_train = y_train.astype(np.compat.long)

# 建立model並初始化
model = SoftmaxClassifier(num_inputs, num_outputs)
criterion = nn.CrossEntropyLoss() # 交叉熵損失
optimizer = optim.SGD(model.parameters(), lr=learning_rate)  # SGD優化器

訓練:

# 遍歷訓練週期數
for epoch in range(num_epochs):
    outputs = model(torch.tensor(X_train))  # 前向傳遞計算
    loss = criterion(outputs,torch.tensor(y_train))  # 計算預測輸出和真實標籤之間的損失
    train_accuracy = model.compute_accuracy(outputs,torch.tensor(y_train))  # 計算模型當前訓練週期中準確率

    optimizer.zero_grad()  # 清楚優化器中梯度
    loss.backward()  # 計算損失對模型引數的梯度
    optimizer.step()
	
    # 列印資訊
    if (epoch + 1) % 10 == 0:
        print(f"Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}, Accuracy: {train_accuracy:.4f}")

執行：

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

生成測試並測試:

X_test, y_test = generate_rand_samples()  # 生成測試資料
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))  # 計算準確度
print(f'Test Accuracy: {accuracy:.4f}')

輸出：

Test Accuracy: 0.9725

繪製影象:

# 繪製影象
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()

感知機分類器

實現與上述softmax分類器相似，此處實現sigmod感知機，採用sigmod作為分類函數，該函數可以將線性變換的結果對映為0到1之間的實數值，通常被用作神經網路中的啟用函數

sigmoid感知機的學習演演算法與普通的感知機類似，也是採用隨機梯度下降（SGD）的方式進行更新。不同之處在於，sigmoid感知機的輸出是一個概率值，需要將其轉化為類別標籤。

通常使用閾值來決定輸出值所屬的類別，如將輸出值大於0.5的樣本歸為正類，小於等於0.5的樣本歸為負類。

定義

# 感知機分類器
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

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

訓練

生成訓練集:

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

# 歸一化資料 將資料特徵減去均值再除以標準差
X_train = (X_train - X_train.mean(axis=0)) / X_train.std(axis=0)

# 建立model並初始化
model = PerceptronClassifier(num_inputs, num_outputs)
optimizer = optim.SGD(model.parameters(), lr=learning_rate)  # SGD優化器

criterion = nn.functional.binary_cross_entropy

訓練：

# 遍歷訓練週期數
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))

# 預測每個點的類別
Z = torch.argmax(model(torch.cat((xx.reshape(-1,1), yy.reshape(-1,1)), 1)), 1)
Z = Z.reshape(xx.shape)

# 繪製分類圖
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral,alpha=0.0)

# 繪製分界線
w = model.linear.weight.detach().numpy()  # 權重
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-')

# 繪製樣本點
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=plt.cm.Spectral)
plt.show()