机器学习_线性回归梯度下降法求解

短命女 2022-12-31 05:18 238阅读 0赞

import numpy as np
    import pandas as pd
    import sklearn.datasets as dataset
    import matplotlib.pyplot as plt
    import matplotlib as mpl
    
    
    class LinearRegression:
        def __init__(self, alpha, times):
            """
            alpha:float
                学习率，用来控制步长(权重调整的幅度)
            times:int
                循环迭代次数
            """
            self.alpha = alpha
            self.times = times
    
        def fit(self, X, y):
            X = np.asarray(X)
            y = np.asarray(y)
            # 创建权重的向量，初始值为零
            self.W_ = np.zeros(1 + X.shape[1])
            # 创建损失列表，用来计算每次
            self.loss = []
            # 进行循环，每次进行迭代计算
            for i in range(self.times):
                y_hat = np.dot(X, self.W_[1:]) + self.W_[0]
                # 计算真实值和预测值之间的差距
                error = y - y_hat
                # 将损失值加入到损失列表
                self.loss.append(np.sum(error ** 2) / 2)
                # 根据差距调整权重w_
                self.W_[0] += self.alpha * np.sum(error)
                self.W_[1:] += self.alpha * np.dot(X.T, error)
    
        def predict(self, X):
            X = np.asarray(X)
            result = np.dot(X, self.W_[1:]) + self.W_[0]
            return result
    
    
    class StandardScaler:
        def fit(self, X):
            X = np.asarray(X)
            self.std = np.std(X, axis=0)
            self.mean = np.mean(X, axis=0)
    
        def transform(self, X):
            return (X - self.mean) / self.std
    
        def fit_transform(self, X):
            self.fit(X)
            return self.transform(X)
    
    
    if __name__ == '__main__':
        boston = dataset.load_boston()
        col_names = np.append(boston.feature_names, 'MEDV')
        data = pd.DataFrame(data=np.c_[boston.data, boston.target], columns=col_names)
    
        data = data.sample(len(data), random_state=0)
        train_x = data.iloc[:400, :-1]
        train_y = data.iloc[:400, -1]
        test_x = data.iloc[400:, :-1]
        test_y = data.iloc[400:, -1]
        S = StandardScaler()
        train_x = S.fit_transform(train_x)
        test_x = S.transform(test_x)
    
        S1 = StandardScaler()
        train_y = S1.fit_transform(train_y)
        test_y = S1.transform(test_y)
        LR = LinearRegression(alpha=0.00005, times=100000)
        # print(train_y)
        LR.fit(train_x, train_y)
    
        result = LR.predict(test_x)
        print(np.mean((result - test_y) ** 2))
        mpl.rcParams['font.family'] = 'SimHei'
        mpl.rcParams['axes.unicode_minus'] = False
        plt.figure(figsize=(10, 10))
        plt.plot(result, 'ro-', label='预测值')
    
        plt.plot(test_y.values, 'go--', label='真实值')
        plt.title('线性回归预测-梯度下降')
        plt.xlabel('样本序号')
        plt.ylabel('房价')
        plt.legend()
        plt.show()
        print(LR.loss)
        m_test = np.array([[1,400,3000],[2,200,4000]])
        print(m_test)
        print(S1.fit_transform(m_test))