Python实现adaboost算法

Adaboost算法是一种集成学习方法，可以用来提高分类器的准确率。下面是用Python实现Adaboost算法的简单示例代码：

from numpy import *
import matplotlib.pyplot as plt

# 构造数据
def loadSimpData():
    datMat = matrix([[1. , 2.1],
                    [2. , 1.1],
                    [1.3, 1. ],
                    [1. , 1. ],
                    [2. , 1. ]])
    classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]
    return datMat,classLabels

# 通过阈值比较对数据进行分类
def stumpClassify(dataMatrix,dimen,threshVal,threshIneq):
    retArray = ones((shape(dataMatrix)[0],1))
    if threshIneq == 'lt':
        retArray[dataMatrix[:,dimen] <= threshVal] = -1.0
    else:
        retArray[dataMatrix[:,dimen] > threshVal] = -1.0
    return retArray

# 找到最佳阈值进行数据分类
def buildStump(dataArr,classLabels,D):
    dataMatrix = mat(dataArr)
    labelMat = mat(classLabels).T
    m,n = shape(dataMatrix)
    numSteps = 10.0
    bestStump = {}
    bestClassEst = mat(zeros((m,1)))
    minError = inf
    for i in range(n):
        rangeMin = dataMatrix[:,i].min()
        rangeMax = dataMatrix[:,i].max()
        stepSize = (rangeMax-rangeMin)/numSteps
        for j in range(-1,int(numSteps)+1):
            for inequal in ['lt', 'gt']:
                threshVal = (rangeMin + float(j) * stepSize)
                predictedVals = stumpClassify(dataMatrix,i,threshVal,inequal)
                errArr = mat(ones((m,1)))
                errArr[predictedVals == labelMat] = 0
                weightedError = D.T*errArr
                if weightedError < minError:
                    minError = weightedError
                    bestClassEst = predictedVals.copy()
                    bestStump['dim'] = i
                    bestStump['thresh'] = threshVal
                    bestStump['ineq'] = inequal
    return bestStump,minError,bestClassEst

# Adaboost算法
def adaBoostTrainDS(dataArr,classLabels,numIt = 40):
    weakClassArr = []
    m = shape(dataArr)[0]
    D = mat(ones((m,1))/m)
    aggClassEst = mat(zeros((m,1)))
    for i in range(numIt):
        bestStump,error,classEst = buildStump(dataArr,classLabels,D)
        alpha = float(0.5*log((1.0-error)/max(error,1e-16)))
        bestStump['alpha'] = alpha
        weakClassArr.append(bestStump)
        expon = multiply(-1*alpha*mat(classLabels).T,classEst)
        D = multiply(D,exp(expon))
        D = D/D.sum()
        aggClassEst += alpha*classEst
        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))
        errorRate = aggErrors.sum()/m
        if errorRate == 0.0: break
    return weakClassArr,aggClassEst

# 绘制数据集和分类结果
def plotResult(dataArr,classLabels,classifier):
    dataMat = array(dataArr)
    n = shape(dataMat)[0]
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(n):
        if classLabels[i] == 1.0:
            xcord1.append(dataMat[i,0])
            ycord1.append(dataMat[i,1])
        else:
            xcord2.append(dataMat[i,0])
            ycord2.append(dataMat[i,1])
    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(min(dataMat[:,0]), max(dataMat[:,0]), 0.1)
    y = arange(min(dataMat[:,1]), max(dataMat[:,1]), 0.1)
    X, Y = meshgrid(x, y)
    Z = zeros(shape(X))
    for i in range(len(x)):
        for j in range(len(y)):
            classLabel = classify([X[i,j], Y[i,j]], classifier)
            Z[i,j] = classLabel
    ax.contourf(X, Y, Z, alpha=0.2)
    plt.show()

# 对输入的数据进行分类
def classify(data,classifiers):
    dataMat = mat(data)
    aggClassEst = 0.0
    for classifier in classifiers:
        classEst = stumpClassify(dataMat,classifier['dim'], \
                                 classifier['thresh'],\
                                 classifier['ineq'])
        aggClassEst += classifier['alpha']*classEst
    return sign(aggClassEst)

# 测试Adaboost算法
def testAdaboost():
    dataArr,classLabels = loadSimpData()
    classifiers,aggClassEst = adaBoostTrainDS(dataArr,classLabels,30)
    plotResult(dataArr,classLabels,classifiers)

if __name__ == '__main__':
    testAdaboost()

以上就是一个简单的Adaboost算法的Python实现示例。注意，Adaboost算法需要通过多个弱分类器来构建一个强分类器，因此在代码中，我们用buildStump()函数来找到最佳阈值进行数据分类，然后用adaBoostTrainDS()函数来训练Adaboost分类器。最后，我们可以用plotResult()函数来绘制分类的结果。