岭回归（ridge regression）

from numpy import *

def loadDataSet(fileName):      #general function to parse tab -delimited floats
    numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields 
    dataMat = []; labelMat = []
    fr = open(fileName)
    for line in fr.readlines():
        lineArr =[]
        curLine = line.strip().split('\t')
        for i in range(numFeat):
            lineArr.append(float(curLine[i]))
        dataMat.append(lineArr)
        labelMat.append(float(curLine[-1]))
    return dataMat,labelMat

def rssError(yArr,yHatArr): #yArr and yHatArr both need to be arrays
    return ((yArr-yHatArr)**2).sum()
    
def ridgeRegres(xMat,yMat,lam=0.2):
    xTx = xMat.T*xMat
    denom = xTx + eye(shape(xMat)[1])*lam
    if linalg.det(denom) == 0.0:
        print ("This matrix is singular, cannot do inverse")
        return
    ws = denom.I * (xMat.T*yMat)
    return ws
    
def ridgeTest(xArr,yArr):
    xMat = mat(xArr)
    yMat=mat(yArr).T
    #数据标准化（归一化）
    yMean = mean(yMat,axis =0)
    yMat = yMat - yMean     #to eliminate X0 take mean off of Y
    print(yMat.shape)
    #regularize X's
    xMat = regularize(xMat)
    
    numTestPts = 30 ###
    wMat = zeros((numTestPts,shape(xMat)[1]))
    for i in range(numTestPts): # 测试不同的lambda时求得的系数矩阵
        ws = ridgeRegres(xMat,yMat,exp(i-10)) #让 labmda 指数变化，广覆盖
        #Y_predict = xMat*ws +yMean
        wMat[i,:]=ws.T #保存不同的lambda时求得各个系数矩阵
    return wMat
    
def regularize(xMat):#regularize by columns
    inMat = xMat.copy()
    inMeans = mean(inMat,axis=0)   #calc mean then subtract it off
    inVar = var(inMat,0)      #calc variance of Xi then divide by it
    inMat = (inMat - inMeans)/inVar #减去均值，再除以标准差
    return inMat

X,Y = loadDataSet("abalone.txt")
ridgeWeights = ridgeTest(X,Y)
print(ridgeWeights.shape)
import matplotlib.pyplot as plt
n = ridgeWeights.shape[1]#特征数
numTestPts = 30 ###
for i in range(n):
    plt.plot(arange(numTestPts)-10, ridgeWeights[:,i], label = "W(%s)"%i)
plt.legend(loc="upper right")
#$\lambda\ $ 注意这里的空格符
plt.title(r"岭回归 回归系数随$\lambda\ $变化规律""\n基于数据集'abalone.txt'", fontsize=16)
plt.xlabel(r"ln($\lambda\ $)")
plt.grid(ls="--",lw =1)
plt.show()

xMat_normilized = regularize(mat(X))
rssErrorList=[]
for i in range(numTestPts):
    Y_predict = xMat_normilized*ridgeWeights[i].reshape(n,1) +mean(mat(Y).T,axis =0)
    RSS = rssError(array(Y).T, array(Y_predict))
    rssErrorList.append(RSS)
plt.plot(arange(numTestPts)-10, rssErrorList)
plt.xlabel(r"ln($\lambda\ $)")
plt.ylabel(r"RSS")
plt.show()
for i in range(20,25):
    Y_predict = xMat_normilized*ridgeWeights[i].reshape(n,1) +mean(mat(Y).T,axis =0)
    RSS = rssError(array(Y).T, array(Y_predict))
    #rssErrorList.append(RSS)
    plt.plot(array(Y)[1000:1100],label= "Y_True(train set)")
    plt.plot(Y_predict[1000:1100], label="Y_Predict")
    plt.title("ln("r"$\lambda\ $"")=%d, RSS =%.1f "%(i-10, RSS))
    plt.legend()
    plt.show()