机器学习python数据集实验

import pandas as pd from matplotlib import pyplot as plt plt.rcParams['font.sans-serif']=['SimHei'] plt.rcParams['axes.unicode_minus'] = False df = pd.read_csv("logisticdata.csv", header=0) # 加载数据集 df.head() # 预览前 5 行数据 print(df) plt.figure(figsize=(10, 6)) plt.scatter(df['X0'],df['X1'], c=df['Y']) plt.title('2021年合肥地区空气状态') plt.show() # Sigmoid 分布函数 def sigmoid(z): sigmoid = 1 / (1 + np.exp(-z)) return sigmoid # 损失函数 def loss(h, y): loss = (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean() return loss # 梯度计算 def gradient(X, h, y): gradient = np.dot(X.T, (h - y)) / y.shape[0] return gradient # 逻辑回归过程 def Logistic_Regression(x, y, lr, num_iter): intercept = np.ones((x.shape[0], 1)) # 初始化截距为 1 x = np.concatenate((intercept, x), axis=1) w = np.zeros(x.shape[1]) # 初始化参数为 0 for i in range(num_iter): # 梯度下降迭代 z = np.dot(x, w) # 线性函数 h = sigmoid(z) # sigmoid 函数 g = gradient(x, h, y) # 计算梯度 w -= lr * g # 通过学习率 lr 计算步长并执行梯度下降 z = np.dot(x, w) # 更新参数到原线性函数中 h = sigmoid(z) # 计算 sigmoid 函数值 l = loss(h, y) # 计算损失函数值 return l, w # 返回迭代后的梯度和参数 """设置参数并训练得到结果 """ import numpy as np x = df[['X0','X1']].values y = df['Y'].values lr = 0.0003 # 学习率 num_iter = 3000 # 迭代次数 # 训练 L = Logistic_Regression(x, y, lr, num_iter) print(L) """将上方得到的结果绘制成图 """ plt.figure(figsize=(10, 6)) plt.scatter(df['X0'],df['X1'], c=df['Y']) x1_min, x1_max = df['X0'].max(), df['X0'].min(), x2_min, x2_max = df['X1'].min(), df['X1'].max(), xx1, xx2 = np.meshgrid(np.linspace(x1_max, x1_min), np.linspace(x2_max, x2_min)) grid = np.c_[xx1.ravel(), xx2.ravel()] probs = (np.dot(grid, np.array([L[1][1:5]]).T) + L[1][0]).reshape(xx1.shape) plt.contour(xx1, xx2, probs, levels=[0], linewidths=1, colors='red'); """绘制损失函数变化曲线 """ def Logistic_Regression(x, y, lr, num_iter): intercept = np.ones((x.shape[0], 1)) # 初始化截距为 1 x = np.concatenate((intercept, x), axis=1) w = np.zeros(x.shape[1]) # 初始化参数为 1 l_list = [] # 保存损失函数值 for i in range(num_iter): # 梯度下降迭代 z = np.dot(x, w) # 线性函数 h = sigmoid(z) # sigmoid 函数 g = gradient(x, h, y) # 计算梯度 w -= lr * g # 通过学习率 lr 计算步长并执行梯度下降 z = np.dot(x, w) # 更新参数到原线性函数中 h = sigmoid(z) # 计算 sigmoid 函数值 l = loss(h, y) # 计算损失函数值 l_list.append(l) return l_list lr = 0.00005 # 学习率 num_iter = 5000 # 迭代次数 l_y = Logistic_Regression(x, y, lr, num_iter) # 训练 # 绘图 plt.figure(figsize=(10, 6)) plt.plot([i for i in range(len(l_y))], l_y) plt.title('空气质量状态逻辑回归') plt.xlabel("迭代次数") plt.ylabel("损失函数") plt.show()