机器学习实战—— Chap08.Regression

向右看齐 2023-06-22 04:21 5阅读 0赞

### Linear Regression ###

import matplotlib.pyplot as plt
    import numpy as np
    
    """
    Desc:
        加载数据
    
    Parameters:
        filename - 文件名
        
    Returns:
        xArr - x数据集
        yArr - y数据集
    """
    def loadDataSet(filename):
        # 计算特征个数，由于最后一列为y值所以减一
        numFeat = len(open(filename).readline().split('\t')) - 1
        xArr = []
        yArr = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = []
            curLine = line.strip().split('\t')
            for i in range(numFeat):
                lineArr.append(float(curLine[i]))
            xArr.append(lineArr)
            yArr.append(float(curLine[-1]))
        return xArr, yArr
    
    
    """
    Desc:
        计算回归系数w
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        
    Returns:
        ws - 回归系数
    """
    def standRegres(xArr, yArr):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        xTx = xMat.T * xMat
        # 求矩阵的行列式
        if np.linalg.det(xTx) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (xTx.I) * (xMat.T) * yMat
        return ws
    
    
    """
    Desc:
        绘制数据集
    
    Parameters:
        None
        
    Returns:
        None
    """
    def plotDataSet():
        xArr, yArr = loadDataSet('ex0.txt')
        ws = standRegres(xArr, yArr)
        xMat = np.mat(xArr)
        yMat = np.mat(yArr)
        xCopy = xMat.copy()
        # 排序
        xCopy.sort(0)
        yHat = xCopy * ws
        # 以下两行是通过corrcoef函数比较预测值和真实值的相关性
        # corrcoef函数得到相关系数矩阵
        # 得到的结果中对角线上的数据是1.0，因为yMat和自己的匹配是完美的
        # 而yHat1和yMat的相关系数为0.98
        yHat1 = xMat * ws
        print(np.corrcoef(yHat1.T, yMat))
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.plot(xCopy[:, 1], yHat, c='red')
        # 绘制样本点即
        # flatten返回一个折叠成一维的数组。但是该函数只能适用于numpy对象，即array或者mat，普通的list列表是不行的
        # 矩阵.A(等效于矩阵.getA())变成了数组
        ax.scatter(xMat[:, 1].flatten().A[0], yMat.flatten().A[0], s=20, c='blue', alpha=.5)
        plt.title('DataSet')
        plt.xlabel('X')
        plt.show()
        
        
    if __name__ == '__main__':
        plotDataSet()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70]

from matplotlib.font_manager import FontProperties
    import matplotlib.pyplot as plt
    import numpy as np
    
    """
    Desc:
        加载数据
    
    Parameters:
        filename - 文件名
        
    Returns:
        xArr - x数据集
        yArr - y数据集
    """
    def loadDataSet(filename):
        # 计算特征个数，由于最后一列为y值所以减一
        numFeat = len(open(filename).readline().split('\t')) - 1
        xArr = []
        yArr = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = []
            curLine = line.strip().split('\t')
            for i in range(numFeat):
                lineArr.append(float(curLine[i]))
            xArr.append(lineArr)
            yArr.append(float(curLine[-1]))
        return xArr, yArr
    
    
    """
    Desc:
        使用局部加权线性回归计算回归系数w
    
    Parameters:
        testPoint - 测试样本点
        xArr - x数据集
        yArr - y数据集
        k - 高斯核的k，自定义参数
        
    Returns:
        ws - 回归系数
    """
    def lwlr(testPoint, xArr, yArr, k=1.0):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        m = np.shape(xMat)[0]
        # 创建加权对角阵
        weights = np.mat(np.eye((m)))
        for j in range(m):
            # 高斯核
            diffMat = testPoint - xMat[j, :]
            weights[j, j] = np.exp(diffMat * diffMat.T / (-2.0 * k**2))
        xTx = xMat.T * (weights * xMat)
        # 求矩阵的行列式
        if np.linalg.det(xTx) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (xTx.I) * (xMat.T * (weights * yMat))
        return testPoint * ws
    
    
    """
    Desc:
        局部加权线性回归测试
    
    Parameters:
        testArr - 测试数据集
        xArr - x数据集
        yArr - y数据集
        k - 高斯核的k,自定义参数
        
    Returns:
        ws - 回归系数
    """
    def lwlrTest(testArr, xArr, yArr, k=1.0):
        m = np.shape(testArr)[0]
        yHat = np.zeros(m)
        for i in range(m):
            yHat[i] = lwlr(testArr[i], xArr, yArr, k)
        return yHat
    
    
    """
    Desc:
        绘制多条局部加权回归曲线
    
    Parameters:
        None
        
    Returns:
        None
    """
    def plotlwlrRegression():
        # 设置中文字体
        font = FontProperties(fname=r"C:\Windows\Fonts\simsun.ttc", size=14)
        xArr, yArr = loadDataSet('ex0.txt')
        yHat_1 = lwlrTest(xArr, xArr, yArr, 1.0)
        yHat_2 = lwlrTest(xArr, xArr, yArr, 0.01)
        yHat_3 = lwlrTest(xArr, xArr, yArr, 0.003)
        xMat = np.mat(xArr)
        yMat = np.mat(yArr)
        # 排序，返回索引值
        srtInd = xMat[:, 1].argsort(0)
        xSort = xMat[srtInd][:, 0, :]
        fig, axs = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=False, figsize=(10, 8))
        axs[0].plot(xSort[:, 1], yHat_1[srtInd], c='red')
        axs[1].plot(xSort[:, 1], yHat_2[srtInd], c='red')
        axs[2].plot(xSort[:, 1], yHat_3[srtInd], c='red')
        axs[0].scatter(xMat[:, 1].flatten().A[0], yMat.flatten().A[0], s=20, c='blue', alpha=.5)
        axs[1].scatter(xMat[:, 1].flatten().A[0], yMat.flatten().A[0], s=20, c='blue', alpha=.5)
        axs[2].scatter(xMat[:, 1].flatten().A[0], yMat.flatten().A[0], s=20, c='blue', alpha=.5)
        axs0_title_text = axs[0].set_title(u'局部加权回归曲线,k=1.0', FontProperties=font)
        axs1_title_text = axs[1].set_title(u'局部加权回归曲线,k=0.01', FontProperties=font)
        axs2_title_text = axs[2].set_title(u'局部加权回归曲线,k=0.003', FontProperties=font)
        plt.setp(axs0_title_text, size=8, weight='bold', color='red')
        plt.setp(axs1_title_text, size=8, weight='bold', color='red')
        plt.setp(axs2_title_text, size=8, weight='bold', color='red')
        plt.xlabel('X')
        plt.show()
        
        
    if __name__ == '__main__':
        plotlwlrRegression()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 1]

import numpy as np
    
    """
    Desc:
        加载数据
    
    Parameters:
        filename - 文件名
        
    Returns:
        xArr - x数据集
        yArr - y数据集
    """
    def loadDataSet(filename):
        # 计算特征个数，由于最后一列为y值所以减一
        numFeat = len(open(filename).readline().split('\t')) - 1
        xArr = []
        yArr = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = []
            curLine = line.strip().split('\t')
            for i in range(numFeat):
                lineArr.append(float(curLine[i]))
            xArr.append(lineArr)
            yArr.append(float(curLine[-1]))
        return xArr, yArr
    
    
    """
    Desc:
        使用局部加权线性回归计算回归系数w
    
    Parameters:
        testPoint - 测试样本点
        xArr - x数据集
        yArr - y数据集
        k - 高斯核的k，自定义参数
        
    Returns:
        ws - 回归系数
    """
    def lwlr(testPoint, xArr, yArr, k=1.0):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        m = np.shape(xMat)[0]
        # 创建加权对角阵
        weights = np.mat(np.eye((m)))
        for j in range(m):
            # 高斯核
            diffMat = testPoint - xMat[j, :]
            weights[j, j] = np.exp(diffMat * diffMat.T / (-2.0 * k**2))
        xTx = xMat.T * (weights * xMat)
        # 求矩阵的行列式
        if np.linalg.det(xTx) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (xTx.I) * (xMat.T * (weights * yMat))
        return testPoint * ws
    
    
    """
    Desc:
        局部加权线性回归测试
    
    Parameters:
        testArr - 测试数据集
        xArr - x数据集
        yArr - y数据集
        k - 高斯核的k,自定义参数
        
    Returns:
        ws - 回归系数
    """
    def lwlrTest(testArr, xArr, yArr, k=1.0):
        m = np.shape(testArr)[0]
        yHat = np.zeros(m)
        for i in range(m):
            yHat[i] = lwlr(testArr[i], xArr, yArr, k)
        return yHat
    
    
    """
    Desc:
        计算回归系数w
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        
    Returns:
        ws - 回归系数
    """
    def standRegres(xArr, yArr):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        xTx = xMat.T * xMat
        # 求矩阵的行列式
        if np.linalg.det(xTx) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (xTx.I) * (xMat.T) * yMat
        return ws
    
    
    """
    Desc:
        误差大小评价函数
    
    Parameters:
        yArr - 真实数据
        yHatArr - 预测数据
        
    Returns:
        ws - 回归系数
    """
    def rssError(yArr, yHatArr):
        return ((yArr - yHatArr)**2).sum()
    
    
    if __name__ == '__main__':
        abX, abY = loadDataSet('abalone.txt')
        print("训练集与测试集相同:局部加权线性回归,核k的大小对预测的影响:")
        yHat01 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 0.1)
        yHat1 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 1)
        yHat10 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 10)
        print('k=0.1时,误差大小为：', rssError(abY[0:99], yHat01.T))
        print('k=1时,误差大小为：', rssError(abY[0:99], yHat1.T))
        print('k=10时,误差大小为：', rssError(abY[0:99], yHat10.T))
        print('')
        print("训练集与测试集不同：局部加权线性回归，核k的大小是越小越好吗？更换数据集，测试结果如下：")
        yHat01 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 0.1)
        yHat1 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 1)
        yHat10 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 10)
        print('k=0.1时,误差大小为：', rssError(abY[100:199], yHat01.T))
        print('k=1时,误差大小为：', rssError(abY[100:199], yHat1.T))
        print('k=10时,误差大小为：', rssError(abY[100:199], yHat10.T))
        print('')
        print("训练集与测试集不同：简单的线性回归与k=1时的局部加权线性回归对比：")
        print('k=1时,误差大小为：', rssError(abY[100:199], yHat1.T))
        ws = standRegres(abX[0:99], abY[0:99])
        yHat = np.mat(abX[100:199]) * ws
        print('简单的线性回归误差大小:', rssError(abY[100:199], yHat.T.A))

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 2]

import numpy as np
    from bs4 import BeautifulSoup
    import random
    
    """
    Desc:
        从页面读取数据，生成retX和retY列表
    
    Parameters:
        retX - 数据X
        retY - 数据Y
        inFile - HTML文件
        yr - 年份
        numPce - 乐高部件数目
        origPrc - 原价
        
    Returns:
        None
    """
    def scrapePage(retX, retY, inFile, yr, numPce, origPrc):
        # 打开并读取HTML文件
        with open(inFile, encoding='utf-8') as f:
            html = f.read()
        soup = BeautifulSoup(html)
        i = 1
        # 根据HTML页面结构进行解析
        currentRow = soup.find_all('table', r='%d' % i)
        while(len(currentRow) != 0):
            currentRow = soup.find_all('table', r='%d' % i)
            title = currentRow[0].find_all('a')[1].text
            lwrTitle = title.lower()
            # 查找是否有全新标签
            if(lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1):
                newFlag = 1.0
            else:
                newFlag = 0.0
            # 查找是否已经标志出售，我们只收集已出售的数据
            soldUnicde = currentRow[0].find_all('td')[3].find_all('span')
            if len(soldUnicde) == 0:
                print("商品#%d没有出售" % i)
            else:
                # 解析页面获取当前价格
                soldPrice = currentRow[0].find_all('td')[4]
                priceStr = soldPrice.text
                priceStr = priceStr.replace('$', '')
                priceStr = priceStr.replace(',', '')
                if len(soldPrice) > 1:
                    priceStr = priceStr.replace('Free shipping', '')
                sellingPrice = float(priceStr)
                # 去掉不完整的套装价格
                if sellingPrice > origPrc * 0.5:
                    print('%d\t%d\t%d\t%f\t%f' % (yr, numPce, newFlag, origPrc, sellingPrice))
                    retX.append([yr, numPce, newFlag, origPrc])
                    retY.append(sellingPrice)
            i += 1
            currentRow = soup.find_all('table', r='%d' % i)
    
    
    """
    Desc:
        依次读取六种乐高套装的数据，并生成数据矩阵
    
    Parameters:
        retX - 数据X
        retY - 数据Y
        
    Returns:
        None
    """
    def setDataCollect(retX, retY):
        # 2006年的乐高8288，部件数目800，原价49.99
        scrapePage(retX, retY, './lego/lego8288.html', 2006, 800, 49.99)
        scrapePage(retX, retY, './lego/lego10030.html', 2002, 3096, 269.99)
        scrapePage(retX, retY, './lego/lego10179.html', 2007, 5195, 499.99)
        scrapePage(retX, retY, './lego/lego10181.html', 2007, 3428, 199.99)
        scrapePage(retX, retY, './lego/lego10189.html', 2008, 5922, 299.99)
        scrapePage(retX, retY, './lego/lego10196.html', 2009, 3263, 249.99)
    
    
    """
    Desc:
        数据标准化
    
    Parameters:
        xMat - x数据集
        yMat - y数据集
        
    Returns:
        inxMat - 标准化后的x数据集
        inyMat - 标准化后的y数据集
    """
    def regularize(xMat, yMat):
        # 深层拷贝
        inxMat = xMat.copy()
        inyMat = yMat.copy()
        # 求yMat的均值
        yMean = np.mean(yMat, 0)
        # 计算yMat每一个值与yMean的差值
        inyMat = yMat - yMean
        # 求inxMat每一列的均值
        inMeans = np.mean(inxMat, 0)
        # 求inxMat每一列的方差即（各项-均值的平方求和）后再除以N
        inVar = np.var(inxMat, 0)
        print(inMeans)
        # 数据减去均值处以方差实现标准化
        inxMat = (inxMat - inMeans) / inVar
        return inxMat, inyMat
    
    
    """
    Desc:
        计算平方误差
    
    Parameters:
        yArr - 预测值
        yHatArr - 真实值
        
    Returns:
        平方误差
    """
    def rssError(yArr, yHatArr):
        return ((yArr - yHatArr)**2).sum()
    
    
    """
    Desc:
        计算回归系数w
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        
    Returns:
        ws - 回归系数
    """
    def standRegres(xArr, yArr):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        xTx = xMat.T * xMat
        # 求矩阵的行列式
        if np.linalg.det(xTx) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (xTx.I) * (xMat.T) * yMat
        return ws
    
    
    """
    Desc:
        岭回归
    
    Parameters:
        xMat - x数据集
        yMat - y数据集
        lam - 缩减系数
        
    Returns:
        ws - 回归系数
    """
    def ridgeRegres(xMat, yMat, lam=0.2):
        xTx = xMat.T * xMat
        demon = xTx + np.eye(np.shape(xMat)[1]) * lam
        # 求矩阵的行列式
        if np.linalg.det(demon) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (demon.I) * (xMat.T) * yMat
        return ws
    
    
    """
    Desc:
        岭回归测试
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        
    Returns:
        wMat - 回归系数矩阵
    """
    def ridgeTest(xArr, yArr):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        # 数据标准化
        # 行与行操作，求均值
        yMean = np.mean(yMat, axis=0)
        # 数据减去均值
        yMat = yMat - yMean
        # 行与行操作，求均值
        xMeans = np.mean(xMat, axis=0)
        # 行与行操作，求方差
        xVar = np.var(xMat, axis=0)
        # 数据减去均值除以方差实现标准化
        xMat = (xMat - xMeans) / xVar
        # 30个不同的lamda测试
        numTestPts = 30
        # 初始化回归系数矩阵
        wMat = np.zeros((numTestPts, np.shape(xMat)[1]))
        # 改变lamda计算回归系数
        for i in range(numTestPts):
            # lamda以e的指数变化，最初是一个非常小的数
            ws = ridgeRegres(xMat, yMat, np.exp(i - 10))
            # 计算回归系数矩阵
            wMat[i, :] = ws.T
        return wMat
    
    
    """
    Desc:
        使用简单的线性回归
    
    Parameters:
        None
        
    Returns:
        None
    """
    def useStandRegres():
        lgX = []
        lgY = []
        setDataCollect(lgX, lgY)
        data_num, features_num = np.shape(lgX)
        # 第一列全为1
        lgx1 = np.mat(np.ones((data_num, features_num+1)))
        lgx1[:, 1:5] = np.mat(lgX)
        # 计算回归系数
        ws = standRegres(lgx1, lgY)
        print("%f%+f*年份%+f*部件数量%+f*是否为全新%+f*原价" % (ws[0], ws[1], ws[2], ws[3], ws[4]))
        
    
    """
    Desc:
        交叉验证岭回归
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        numVal - 交叉验证次数
        
    Returns:
        wMat - 回归系数矩阵
    """
    def crossValidation(xArr, yArr, numVal=10):
        m = len(yArr)
        indexList = list(range(m))
        errorMat = np.zeros((numVal, 30))
        for i in range(numVal):
            trainX = []
            trainY = []
            testX = []
            testY = []
            # shuffle() 方法将序列的所有元素随机排序。
            random.shuffle(indexList)
            for j in range(m):
                # 90%数据训练集
                if j < m * 0.9:
                    trainX.append(xArr[indexList[j]])
                    trainY.append(yArr[indexList[j]])
                # 10%数据测试集
                else:
                    testX.append(xArr[indexList[j]])
                    testY.append(yArr[indexList[j]])
            # 岭回归测试
            wMat = ridgeTest(trainX, trainY)
            for k in range(30):
                matTestX = np.mat(testX)
                matTrainX = np.mat(trainX)
                # 标准化
                meanTrain = np.mean(matTrainX, 0)
                varTrain = np.var(matTrainX, 0)
                matTestX = (matTestX - meanTrain) / varTrain
                # 数据还原
                yEst = matTestX * np.mat(wMat[k, :]).T + np.mean(trainY)
                errorMat[i, k] = rssError(yEst.T.A, np.array(testY))
        meanErrors = np.mean(errorMat, 0)
        minMean = float(min(meanErrors))
        bestWeights = wMat[np.nonzero(meanErrors == minMean)]
        # 表转换
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        meanX = np.mean(xMat, 0)
        varX = np.var(xMat, 0)
        unReg = bestWeights / varX
        print("%f%+f*年份%+f*部件数量%+f*是否为全新%+f*原价" % ((-1 * np.sum(np.multiply(meanX, unReg)) + np.mean(yMat)), unReg[0, 0], unReg[0, 1], unReg[0, 2], unReg[0, 3]))
        
     
    if __name__ == '__main__':
        # useStandRegres()
        lgX = []
        lgY = []
        setDataCollect(lgX, lgY)
        print(ridgeTest(lgX, lgY))
        crossValidation(lgX, lgY)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 3]

### Ridge Regression ###

from matplotlib.font_manager import FontProperties
    import matplotlib.pyplot as plt
    import numpy as np
    
    """
    Desc:
        加载数据
    
    Parameters:
        filename - 文件名
        
    Returns:
        xArr - x数据集
        yArr - y数据集
    """
    def loadDataSet(filename):
        # 计算特征个数，由于最后一列为y值所以减一
        numFeat = len(open(filename).readline().split('\t')) - 1
        xArr = []
        yArr = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = []
            curLine = line.strip().split('\t')
            for i in range(numFeat):
                lineArr.append(float(curLine[i]))
            xArr.append(lineArr)
            yArr.append(float(curLine[-1]))
        return xArr, yArr
    
    
    """
    Desc:
        岭回归
    
    Parameters:
        xMat - x数据集
        yMat - y数据集
        lam - 缩减系数
        
    Returns:
        ws - 回归系数
    """
    def ridgeRegres(xMat, yMat, lam=0.2):
        xTx = xMat.T * xMat
        demon = xTx + np.eye(np.shape(xMat)[1]) * lam
        # 求矩阵的行列式
        if np.linalg.det(demon) == 0.0:
            print("矩阵为奇异矩阵，不能求逆")
            return
        # .I求逆矩阵
        ws = (demon.I) * (xMat.T) * yMat
        return ws
    
    
    """
    Desc:
        岭回归测试
    
    Parameters:
        xArr - x数据集
        yArr - y数据集
        
    Returns:
        wMat - 回归系数矩阵
    """
    def ridgeTest(xArr, yArr):
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        # 数据标准化
        # 行与行操作，求均值
        yMean = np.mean(yMat, axis=0)
        # 数据减去均值
        yMat = yMat - yMean
        # 行与行操作，求均值
        xMeans = np.mean(xMat, axis=0)
        # 行与行操作，求方差
        xVar = np.var(xMat, axis=0)
        # 数据减去均值除以方差实现标准化
        xMat = (xMat - xMeans) / xVar
        # 30个不同的lamda测试
        numTestPts = 30
        # 初始化回归系数矩阵
        wMat = np.zeros((numTestPts, np.shape(xMat)[1]))
        # 改变lamda计算回归系数
        for i in range(numTestPts):
            # lamda以e的指数变化，最初是一个非常小的数
            ws = ridgeRegres(xMat, yMat, np.exp(i - 10))
            # 计算回归系数矩阵
            wMat[i, :] = ws.T
        return wMat
    
    
    """
    Desc:
        绘制岭回归系数矩阵
    
    Parameters:
        None
        
    Returns:
        None
    """
    def plotwMat():
        # 设置中文字体
        font = FontProperties(fname=r"C:\Windows\Fonts\simsun.ttc", size=14)
        abX, abY = loadDataSet('abalone.txt')
        redgeWeights = ridgeTest(abX, abY)
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.plot(redgeWeights)
        ax_title_text = ax.set_title(u'log(lamda)与回归系数的关系', FontProperties=font)
        ax_xlabel_text = ax.set_xlabel(u'log(lamda)', FontProperties=font)
        ax_ylabel_text = ax.set_ylabel(u'回归系数', FontProperties=font)
        plt.setp(ax_title_text, size=20, weight='bold', color='red')
        plt.setp(ax_xlabel_text, size=20, weight='bold', color='black')
        plt.setp(ax_ylabel_text, size=20, weight='bold', color='black')
        plt.show()
    
    
    if __name__ == '__main__':
        plotwMat()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 4]

from matplotlib.font_manager import FontProperties
    import matplotlib.pyplot as plt
    import numpy as np
    
    """
    Desc:
        加载数据
    
    Parameters:
        filename - 文件名
        
    Returns:
        xArr - x数据集
        yArr - y数据集
    """
    def loadDataSet(filename):
        # 计算特征个数，由于最后一列为y值所以减一
        numFeat = len(open(filename).readline().split('\t')) - 1
        xArr = []
        yArr = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = []
            curLine = line.strip().split('\t')
            for i in range(numFeat):
                lineArr.append(float(curLine[i]))
            xArr.append(lineArr)
            yArr.append(float(curLine[-1]))
        return xArr, yArr
    
    
    """
    Desc:
        数据标准化
    
    Parameters:
        xMat - x数据集
        yMat - y数据集
        
    Returns:
        inxMat - 标准化后的x数据集
        inyMat - 标准化后的y数据集
    """
    def regularize(xMat, yMat):
        inxMat = xMat.copy()
        inyMat = yMat.copy()
        # 求yMat的均值
        yMean = np.mean(yMat, 0)
        # 计算yMat每一个值与yMean的差值
        inyMat = yMat - yMean
        # 求inxMat每一列的均值
        inMeans = np.mean(inxMat, 0)
        # 求inxMat每一列的方差即（各项-均值的平方求和）后再除以N
        inVar = np.var(inxMat, 0)
        # 数据减去均值处以方差实现标准化
        inxMat = (inxMat - inMeans) / inVar
        return inxMat, inyMat
    
    
    """
    Desc:
        计算平方误差
    
    Parameters:
        yArr - 预测值
        yHatArr - 真实值
        
    Returns:
        平方误差
    """
    def rssError(yArr, yHatArr):
        return ((yArr - yHatArr)**2).sum()
    
    
    """
    Desc:
        前向逐步线性回归
    
    Parameters:
        xArr - x输入数据
        yArr - y输入数据
        eps - 每次迭代需要调整的步长
        numIt - 迭代次数
        
    Returns:
        returnMat - numIt次迭代的回归系数矩阵
    """
    def stageWise(xArr, yArr, eps=0.01, numIt=100):
        # 使xMat和yMat的行数一致
        xMat = np.mat(xArr)
        yMat = np.mat(yArr).T
        # 标准化
        xMat, yMat = regularize(xMat, yMat)
        m, n = np.shape(xMat)
        returnMat = np.zeros((numIt, n))
        ws = np.zeros((n, 1))
        wsTest = ws.copy()
        wsMax = ws.copy()
        for i in range(numIt):
            lowestError = float('inf')
            for j in range(n):
                for sign in [-1, 1]:
                    wsTest = ws.copy()
                    # 微调回归系数
                    wsTest[j] += eps * sign
                    # 计算预测值
                    yTest = xMat * wsTest
                    # 计算平方误差
                    rssE = rssError(yMat.A, yTest.A)
                    # 如果误差更小则更新当前的最佳回归系数
                    if rssE < lowestError:
                        lowestError = rssE
                        wsMax = wsTest
            ws = wsMax.copy()
            # 记录numIt次迭代的回归系数矩阵
            returnMat[i, :] = ws.T
        return returnMat
    
    
    """
    Desc:
        绘制岭回归系数矩阵
    
    Parameters:
        None
        
    Returns:
        None
    """
    def plotstageWiseMat():
        # 设置中文字体
        font = FontProperties(fname=r"C:\Windows\Fonts\simsun.ttc", size=14)
        xArr, yArr = loadDataSet('abalone.txt')
        returnMat = stageWise(xArr, yArr, 0.005, 1000)
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.plot(returnMat)
        ax_title_text = ax.set_title(u'前向逐步回归：迭代次数与回归系数的关系', FontProperties=font)
        ax_xlabel_text = ax.set_xlabel(u'迭代次数', FontProperties=font)
        ax_ylabel_text = ax.set_ylabel(u'回归系数', FontProperties=font)
        plt.setp(ax_title_text, size=15, weight='bold', color='red')
        plt.setp(ax_xlabel_text, size=10, weight='bold', color='black')
        plt.setp(ax_ylabel_text, size=10, weight='bold', color='black')
        plt.show()
    
    
    if __name__ == '__main__':
        plotstageWiseMat()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 5]

from sklearn import linear_model
    from bs4 import BeautifulSoup
    
    """
    Desc:
        从页面读取数据，生成retX和retY列表
    
    Parameters:
        retX - 数据X
        retY - 数据Y
        inFile - HTML文件
        yr - 年份
        numPce - 乐高部件数目
        origPrc - 原价
        
    Returns:
        None
    """
    def scrapePage(retX, retY, inFile, yr, numPce, origPrc):
        # 打开并读取HTML文件
        with open(inFile, encoding='utf-8') as f:
            html = f.read()
        soup = BeautifulSoup(html)
        i = 1
        # 根据HTML页面结构进行解析
        currentRow = soup.find_all('table', r='%d' % i)
        while(len(currentRow) != 0):
            currentRow = soup.find_all('table', r='%d' % i)
            title = currentRow[0].find_all('a')[1].text
            lwrTitle = title.lower()
            # 查找是否有全新标签
            if(lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1):
                newFlag = 1.0
            else:
                newFlag = 0.0
            # 查找是否已经标志出售，我们只收集已出售的数据
            soldUnicde = currentRow[0].find_all('td')[3].find_all('span')
            if len(soldUnicde) == 0:
                print("商品#%d没有出售" % i)
            else:
                # 解析页面获取当前价格
                soldPrice = currentRow[0].find_all('td')[4]
                priceStr = soldPrice.text
                priceStr = priceStr.replace('$', '')
                priceStr = priceStr.replace(',', '')
                if len(soldPrice) > 1:
                    priceStr = priceStr.replace('Free shipping', '')
                sellingPrice = float(priceStr)
                # 去掉不完整的套装价格
                if sellingPrice > origPrc * 0.5:
                    print('%d\t%d\t%d\t%f\t%f' % (yr, numPce, newFlag, origPrc, sellingPrice))
                    retX.append([yr, numPce, newFlag, origPrc])
                    retY.append(sellingPrice)
            i += 1
            currentRow = soup.find_all('table', r='%d' % i)
    
    
    """
    Desc:
        依次读取六种乐高套装的数据，并生成数据矩阵
    
    Parameters:
        retX - 数据X
        retY - 数据Y
        
    Returns:
        None
    """
    def setDataCollect(retX, retY):
        # 2006年的乐高8288，部件数目800，原价49.99
        scrapePage(retX, retY, './lego/lego8288.html', 2006, 800, 49.99)
        scrapePage(retX, retY, './lego/lego10030.html', 2002, 3096, 269.99)
        scrapePage(retX, retY, './lego/lego10179.html', 2007, 5195, 499.99)
        scrapePage(retX, retY, './lego/lego10181.html', 2007, 3428, 199.99)
        scrapePage(retX, retY, './lego/lego10189.html', 2008, 5922, 299.99)
        scrapePage(retX, retY, './lego/lego10196.html', 2009, 3263, 249.99)
        
    
    """
    Desc:
        使用sklearn
    
    Parameters:
        None
        
    Returns:
        None
    """
    def usesklearn():
        reg = linear_model.Ridge(alpha=.5)
        lgX = []
        lgY = []
        setDataCollect(lgX, lgY)
        # fit(X, y):Fit Ridge regression model
        reg.fit(lgX, lgY)
        print("%f%+f*年份%+f*部件数量%+f*是否为全新%+f*原价" % (reg.intercept_, reg.coef_[0], reg.coef_[1], reg.coef_[2], reg.coef_[3]))
    
    
    if __name__ == '__main__':
        usesklearn()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 6]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20191213201105376.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70
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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/20191213201218481.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 3]: https://img-blog.csdnimg.cn/20191213201305758.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 4]: https://img-blog.csdnimg.cn/20191213201518254.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 5]: https://img-blog.csdnimg.cn/20191213201547453.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ_size_16_color_FFFFFF_t_70 6]: https://img-blog.csdnimg.cn/20191213201648511.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MTcyODQzMQ==,size_16,color_FFFFFF,t_70