机器学习（吴恩达） python练习笔记第一周

布满荆棘的人生 2023-06-18 06:59 11阅读 0赞

## 一元线性回归方程： ##

from sklearn.linear_model import LinearRegression
    import numpy as np
    import matplotlib.pyplot as plt
    import pandas as pd
    from sklearn.model_selection import train_test_split
    
    # 创建数据集
    examDict = { '面积':[2000,2050,1000,980,500,520,400,450,300,200,100,1080,1520,580,900,1050,250],
                '价格':[1050,1000,520,520,260,270,220,240,140,110,60,500,780,280,450,510,125]}
    examDf = pd.DataFrame(examDict)
    # print(examDf)
    
    # # 绘制散点图
    # plt.scatter(examDf.面积 ,examDf.价格, color='b', label='Exam Data')
    # # 添加图的标签（x轴，y轴）
    # plt.xlabel('area')
    # plt.ylabel('price')
    # # plt.show()
    
    # 相关系数R r(相关系数) = x和y的协方差/(x的标准差*y的标准差) == cov（x,y）/σx*σy（即person系数）
    rDf = examDf.corr()
    print(rDf)
    
    # 将原始数据集拆分为训练集和测试集
    exam_X = examDf.面积
    exam_y = examDf.价格
    X_train,X_test,y_train,y_test = train_test_split(exam_X, exam_y, train_size=.8, test_size=.2)
    # print("原始数据特征:", exam_X.shape(), ",训练数据特征:", X_train.shape(), "测试数据特征：", X_test.shape())
    # print("原始数据标签:", exam_y.shape(),",训练数据标签:",y_train.shape(),"测试数据标签：",y_test.shape())
    plt.scatter(X_train, y_train, color='b', label='train data')
    plt.scatter(X_test, y_test, color='r', label='test data')
    plt.legend(loc=2)
    plt.xlabel('area')
    plt.ylabel('price')
    plt.savefig('tests.png')
    # plt.show()
    
    # 将训练集放入线性回归模型进行训练
    lr = LinearRegression()
    X_train = X_train.values.reshape(-1,1)
    y_train = y_train.values.reshape(-1,1)
    X_test = X_test.values.reshape(-1,1)
    y_test = y_test.values.reshape(-1,1)
    lr.fit(X_train,y_train)
    
    a = lr.coef_ # 回归系数
    b = lr.intercept_ # 截距
    print("y=",a,"x+",b)
    
    y_train_hat = lr.predict(X_train) # 训练数据的预测值
    print("y_hat:",y_train_hat)
    # 绘制拟合线
    plt.plot(X_train, y_train_hat, color='black', linewidth=3, label='best line')
    # 测试数据散点图
    plt.plot(X_test, y_test, color='red', label='test data')
    plt.legend(loc=2)
    plt.xlabel('area')
    plt.ylabel('price')
    plt.savefig('lines.png')
    plt.show()
    print('测试集相关系数:', lr.score(X_test,y_test))
    
    
    # 假设函数
    def hypothesis(theta0, theta1, x):
        return theta1*x + theta0
    # 代价函数
    def Cost_Function(theta0, theta1, x, y):
        m = 4
        return 0.5/m * (np.square(theta1*x + theta0 - y)).sum()
    # 优化函数
    def optimize(theta0, theta1, x, y):
        m = 4
        alpha = 1
        y_hat = hypothesis(theta0, theta1, x)
        d_theta0 = 1/m * ((y_hat - y).sum())
        d_theta1 = 1/m * (((y_hat - y)*x).sum())
        theta0 = theta0 - alpha*d_theta0
        theta1 = theta1 - alpha*d_theta1
        return theta0, theta1

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzMzNTYyOTgy_size_16_color_FFFFFF_t_70]

## 矩阵（单位阵，矩阵乘法，转置，求逆）： ##

import numpy as np
    
    A = np.array([[1,2],[4,5]])
    # A = np.reshape(A, newshape=(2,2))
    B = np.array([[1,1],[0,2]])
    # B = np.reshape(B, newshape=(2,2))
    print(A)
    print(B)
    # 单位矩阵
    I = np.eye(2)
    print(I)
    # 矩阵乘法：满足结合律不满足交换律
    # dot为矩阵点乘，multiply为矩阵*乘即对应位置的元素相乘
    IA = np.dot(I,A)
    AI = np.dot(A,I)
    AB = np.dot(A,B)
    BA = np.dot(B,A)
    print(IA)
    print(AI)
    print(AB)
    print(BA)
    
    C = np.array([[1,2,0], [0,5,6], [7,0,9]])
    # A的转置矩阵
    C_trans = C.T
    print(C_trans)
    # 矩阵的逆
    C_inv = np.linalg.inv(C)
    print(C_inv)
    I = np.dot(C, C_inv)
    # 设置输出矩阵的小数点位数
    np.set_printoptions(formatter={ 'float':'{:0.2f}'.format})
    print(I)
    
    # transpose实现多维度变换
    data = np.arange(24).reshape(2,3,4) # 2个3×4的矩阵
    print(data)
    print(data.transpose(1,0,2)) # 2,3,4三个参数分别对应0,1,2,交换后为3个2×4的矩阵
    # swapaxes两轴对换
    print(data.swapaxes(0,1)) # 实现2,3两个参数对换

## 多元线性回归方程 ##

from sklearn.linear_model import LinearRegression
    import numpy as np
    import matplotlib.pyplot as plt
    import pandas as pd
    from sklearn.model_selection import train_test_split
    # import seaborn as sn
    # 创建数据集
    examDict = { 'areas':[2000,2050,1000,980,500,520,400,450,300,200,100,1080,1520,580,900,1050,250],
                'numberofrooms':[10,10,5,4,3,3,2,3,2,1,1,5,7,3,4,5,1],
                'price':[1050,1000,520,520,260,270,220,240,140,110,60,500,780,280,450,510,125]}
    examDf = pd.DataFrame(examDict)
    
    # 得到所需要的数据集且查看前几列以及数据形状
    print('head:', examDf.head())
    # 数据描述
    print(examDf.describe())
    # 缺失值检验
    print(examDf[examDf.isnull()==True].count())
    
    examDf.boxplot()
    plt.savefig('boxplot.png')
    plt.show()
    
    # 相关系数R r(相关系数) = x和y的协方差/(x的标准差*y的标准差) == cov（x,y）/σx*σy（即person系数）
    print(examDf.corr())
    
    # # 通过加入一个参数kind='reg'，seaborn可以添加一条最佳拟合直线和95%的置信带
    # sns.pairplot(examDf, x_vars=['areas','number of rooms'], y_vars='price',size=7,aspect=0.8,kind='reg')
    # plt.savefig("pairplot.png")
    # plt.show()
    
    # print(examDf.ix[:,:2])表示前两个特征
    X_train, X_test, y_train, y_test = train_test_split(examDf.ix[:,:2], examDf.price, train_size=.8, test_size=.2)
    lr = LinearRegression()
    # X_train = X_train.values.reshape(-1,1)
    # y_train = y_train.values.reshape(-1,1)
    # X_test = X_test.values.reshape(-1,1)
    # y_test = y_test.values.reshape(-1,1)
    lr.fit(X_train, y_train)
    print("回归系数：",lr.coef_,"/n截距：",lr.intercept_)
    print("R方检测分数:",lr.score(examDf.ix[:,:2],examDf.price))
    
    # 对先行回归进行预测
    y_hat = lr.predict(X_test)
    print("y_hat:",y_hat)
    
    # 绘图
    plt.figure()
    plt.plot(range(len(y_hat)), y_hat, color='b', label='predict')
    plt.plot(range(len(y_hat)), y_test, color='r', label='test')
    plt.legend(loc='upper right')
    plt.xlabel('futures')
    plt.ylabel('price')
    plt.savefig('predict.png')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzMzNTYyOTgy_size_16_color_FFFFFF_t_70 1]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzMzNTYyOTgy_size_16_color_FFFFFF_t_70 2]  
参考文章：  
https://blog.csdn.net/weixin\_40014576/article/details/79918819\#commentBox

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