前言

代码实现

import numpy as np


# 初始数据
def loadSimpData():
    dataMat = np.array([
        [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 dataMat, classLabels


def stumpClassify(dataMatrix, dimen, threshVal, threshIneq):
    """
    对数据进行分类哦
    :param dataMatrix: 数据矩阵
    :param dimen: 即对哪一列的数据进行处理
    :param threshVal: 阈值
    :param threshIneq: 标识符，即需要设置为-1的数据是大于阈值还是小于阈值
    :return: 返回数据的类别矩阵
    """
    # 创建形状为（样本个数, 1）形状的反馈矩阵，初始化为1
    retArray = np.ones((np.shape(dataMatrix)[0], 1))
    if threshIneq == 'lt':
        retArray[dataMatrix[:, dimen] <= threshVal] = -1.0
    else:
        retArray[dataMatrix[:, dimen] > threshVal] = -1.0
    return retArray


def buildStump(dataArr, classLabels, D):
    """
    找到数据集上面最佳单层决策树
    :param dataArr: 样本矩阵
    :param classLabels: 标签
    :param D: 权重矩阵
    :return: 最佳单层决策树的相关变量
    """
    dataMatrix = np.mat(dataArr)
    labelMat = np.mat(classLabels).T
    # m：样本总数，n：列数
    m, n = np.shape(dataMatrix)
    numSteps = 10.0
    bestStump = {}
    bestClasEst = np.mat(np.zeros((m, 1)))
    minError = np.inf
    # 遍历所有特征
    for i in range(n):
        # 获取该列的最大和最小值
        rangeMin = dataMatrix[:, i].min()
        rangeMax = dataMatrix[:, i].max()
        # 计算步长
        stepSize = (rangeMax - rangeMin) / numSteps
        for j in range(-1, int(numSteps) + 1):
            # 对该特征的不同值进行遍历
            for inequal in ['lt', 'gt']:
                # 获取阈值
                threshVal = (rangeMin + float(j) * stepSize)
                # 对该特征的值进行分类
                predictedVals = stumpClassify(dataMatrix, i, threshVal, inequal)
                errArr = np.mat(np.ones((m, 1)))
                errArr[predictedVals == labelMat] = 0
                weightError = D.T * errArr
                # 计算加权错误率
                print("split: dim %d, thresh %.2f, thresh inequal: %s, the weightederror is %.3f" % (i, threshVal, inequal, weightError))
                if weightError < minError:
                    minError = weightError
                    bestClasEst = predictedVals.copy()
                    bestStump['dim'] = i
                    bestStump['thresh'] = threshVal
                    bestStump['ineq'] = inequal
    # bestStump：最佳单层决策树；minError：最小错误率；bestClassEst：估计的类别向量：
    return bestStump, minError, bestClasEst


def adaBoostTrainDS(dataArr, classLabels, numIt=40):
    # 弱分类器数组
    weakClassArr = []
    # 获取样本数
    m = np.shape(dataArr)[0]
    # 设置权重
    D = np.mat(np.ones((m, 1))/m)
    aggClassEst = np.mat(np.zeros((m, 1)))
    for i in range(numIt):
        bestStump, error, classEst = buildStump(dataArr, classLabels, D)
        print("D:", D.T)
        alpha = float(0.5 * np.log((1.0 - error) / max(error, 1e-16)))
        bestStump['alpha'] = alpha
        weakClassArr.append(bestStump)
        print("classEst:", classEst.T)
        # 为下一次迭代计算D
        expon = np.multiply(-1 * alpha * np.mat(classLabels).T, classEst)
        D = np.multiply(D, np.exp(expon))
        D = D / D.sum()
        # 错误率累加计算
        aggClassEst += alpha * classEst
        print("aggClassEst:", aggClassEst.T)
        aggError = np.multiply(np.sign(aggClassEst) != np.mat(classLabels).T, np.ones((m, 1)))
        errorRate = aggError.sum() / m
        print("total error:", errorRate, "\n")
        if errorRate == 0.0:
            break
    return weakClassArr


def adaClassify(datToClass, classifierArr):
    dataMatrix = np.mat(datToClass)
    m = np.shape(dataMatrix)[0]
    aggClassEst = np.mat(np.zeros((m, 1)))
    for i in range(len(classifierArr)):
        classEst = stumpClassify(dataMatrix, classifierArr[i]['dim'], classifierArr[i]['thresh'], classifierArr[i]['ineq'])
        aggClassEst += classifierArr[i]['alpha'] * classEst
        print(aggClassEst)
    return np.sign(aggClassEst)


if __name__ == "__main__":
    datMat, classLabels = loadSimpData()
    # D = np.mat(np.ones((5, 1))/5)
    # buildStump(datMat, classLabels, D)
    # print(np.shape(datMat[0]))
    classifierArray = adaBoostTrainDS(datMat, classLabels, 30)
    # adaClassify([0, 0], classifierArray)
    result = adaClassify([[5, 5], [0, 0]], classifierArray)
    print(result)