逻辑回归函数定义

逻辑回归

sigmoid求导

假设

公示整合

似然函数

对数似然

求导

梯度上升

%matplotlib inline
from numpy import *
#导入数据并整理
def loadDataSet(fileName):
    dataMat = []
    labelMat = []
    fr = open(fileName)
    for line in fr.readlines():
        lineArr = line.strip().split()
        dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
        labelMat.append(float(lineArr[2]))
    return dataMat,labelMat

#sigmoid函数
def sigmoid(inX):
    return 1.0/(1+exp(-inX))

#画图
def plotBestFit(weights):
    import matplotlib.pyplot as plt
    dataMat,labelMat=loadDataSet('testSet.txt')
    dataArr = array(dataMat)
    n = shape(dataArr)[0] 
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(n):
        if int(labelMat[i])== 1:
            xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])
        else:
            xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
    ax.scatter(xcord2, ycord2, s=30, c='green')
    x = arange(-3.0, 3.0, 0.1)
    y = (-weights[0]-weights[1]*x)/weights[2]
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()

#批梯度上升
def gradAscent(dataMatIn,classLabels,alpha = 0.001,maxCycles = 500):
    dataMatrix = mat(dataMatIn)
    labelMat = mat(classLabels).transpose()
    m,n = shape(dataMatrix)
    weights = ones((n,1))
    for k in range(maxCycles):
        h = sigmoid(dataMatrix * weights)
        error = labelMat - h
        weights = weights + alpha * dataMatrix.transpose()*error
    return weights

#测试
dataArr,labelArr = loadDataSet('testSet.txt')
weights = gradAscent(dataArr,labelArr,0.001,500)
plotBestFit(weights.getA())

批梯度上升

#随机梯度上升
def stocGradAscent(dataMatrix, classLabels, numIter=150):
    m,n=shape(dataMatrix)
    weights=ones(n)
    for j in range(numIter):
        dataIndex=range(m)
        for i in range(m):
            alpha=4/(1.0+j+i)+0.01
            randIndex=int(random.uniform(0,len(dataIndex)))
            h=sigmoid(sum(dataMatrix[randIndex]*weights))
            error=classLabels[randIndex]-h
            weights=weights+alpha*error*dataMatrix[randIndex]
            del[dataIndex[randIndex]]
    return weights

dataArr,labelMat = loadDataSet('testSet.txt')
weights = stocGradAscent(array(dataArr),labelMat,500)
plotBestFit(weights)

随机梯度上升

spark代码示例

public class LogisticWithElasticNet {
    /**
     * 日志控制
     */
    static{
        LogSetting.setWarningLogLevel("org");
        LogSetting.setWarningLogLevel("akka");
        LogSetting.setWarningLogLevel("io");
        LogSetting.setWarningLogLevel("httpclient.wire");
    }

    public static void main(String[] args) {
        String resources = Thread.currentThread().getContextClassLoader().getResource("").getPath();
        SparkConf conf = new SparkConf().setAppName("Logistic Regression with Elastic Net Example").setMaster("local[2]");
        SparkContext sc = new SparkContext(conf);
        SQLContext sqlContext = new SQLContext(sc);

        String path  = resources + "libsvm_data.txt";
        DataFrame training = sqlContext.read().format("libsvm").load(path);

        LogisticRegression lr = new LogisticRegression()
                .setMaxIter(10)
                .setRegParam(0.3)
                .setElasticNetParam(0.8);

        // Fit the model
        LogisticRegressionModel lrModel = lr.fit(training);

        System.out.println("Coefficients: "
                + lrModel.coefficients() + " Intercept: " + lrModel.intercept());

        // Extract the summary from the returned LogisticRegressionModel instance trained in the earlier example
        LogisticRegressionTrainingSummary trainingSummary = lrModel.summary();

        // Obtain the loss per iteration.
        double[] objectiveHistory = trainingSummary.objectiveHistory();
        for (double lossPerIteration : objectiveHistory) {
            System.out.println(lossPerIteration);
        }

        // Obtain the metrics useful to judge performance on test data.
        // We cast the summary to a BinaryLogisticRegressionSummary since the problem is a binary classification problem.
        BinaryLogisticRegressionSummary binarySummary =
                (BinaryLogisticRegressionSummary) trainingSummary;

        // Obtain the receiver-operating characteristic as a dataframe and areaUnderROC.
        DataFrame roc = binarySummary.roc();
        roc.show();
        roc.select("FPR").show();
        System.out.println(binarySummary.areaUnderROC());

        // Get the threshold corresponding to the maximum F-Measure and rerun LogisticRegression with this selected threshold.
        DataFrame fMeasure = binarySummary.fMeasureByThreshold();
        double maxFMeasure = fMeasure.select(functions.max("F-Measure")).head().getDouble(0);
        double bestThreshold = fMeasure.where(fMeasure.col("F-Measure").equalTo(maxFMeasure))
                .select("threshold").head().getDouble(0);
        lrModel.setThreshold(bestThreshold);
    }
}