import numpy as np # 生成模拟数据 np.random.seed(42) X = np.random.randn(100, 2) # 100...

import numpy as np # 生成模拟数据 np.random.seed(42) X = np.random.randn(100, 2) # 100个样本，每个样本两个特征 y = (X[:, 0] + X[:, 1] > 0).astype(int) # 如果x1 + x2 > 0，则分类为1，否则分类为0 # 定义 Sigmoid 函数 def sigmoid(z): return 1 / (1 + np.exp(-z)) # 初始化参数 np.random.seed(42) W = np.random.randn(2) # 权重维度与特征维度一致 b = 0 # 偏置 learning_rate = 0.1 num_iterations = 1000 # 梯度下降优化 for i in range(num_iterations): # 计算预测值 z = np.dot(X, W) + b y_pred = sigmoid(z) # 计算损失（对数损失） loss = -np.mean(y * np.log(y_pred + 1e-8) + (1 - y) * np.log(1 - y_pred + 1e-8)) # 计算梯度 dw = np.dot(X.T, (y_pred - y)) / len(y) db = np.mean(y_pred - y) # 更新参数 W -= learning_rate * dw b -= learning_rate * db # 每隔100次打印一次损失 if i % 100 == 0: print(f"Iteration {i}, Loss: {loss:.4f}") # 绘制决策边界 import matplotlib.pyplot as plt plt.scatter(X[:, 0], X[:, 1], c=y, cmap="viridis") x_boundary = np.linspace(-3, 3, 100) y_boundary = -(b + W[0] * x_boundary) / W[1] plt.plot(x_boundary, y_boundary, color="red") plt.xlabel("x1") plt.ylabel("x2") plt.title("决策边界") plt.show()