机器学习实战—— Chap07.AdaBoost

import numpy as np
import matplotlib.pyplot as plt

"""
Desc:
    创建单层决策树的数据集

Parameters:
    None
    
Returns:
    dataMat - 数据矩阵
    classLabels - 数据标签
"""
def loadsimpData():
    datMat = np.matrix([[1. , 2.1],
                        [1.5, 1.6],
                        [1.3, 1. ],
                        [1. , 1. ],
                        [2. , 1. ]])
    classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]
    return datMat, classLabels


"""
Desc:
    单层决策树分类函数

Parameters:
    dataMatrix - 数据矩阵
    dimen - 第dimen列，也就是第几个特征
    threshVal - 阈值
    threshIneq - 标志
    
Returns:
    retArray - 分类结果
"""
def stumpClassify(dataMatrix, dimen, threshVal, threshIneq):
    # 初始化retArray为全1列向量
    retArray = np.ones((np.shape(dataMatrix)[0], 1))
    if threshIneq == 'lt':
        # 如果小于阈值则赋值为-1
        retArray[dataMatrix[:, dimen] <= threshVal] = -1.0
    else:
        # 如果大于阈值则赋值为-1
        retArray[dataMatrix[:, dimen] > threshVal] = -1.0
    return retArray


"""
Desc:
    找到数据集上最佳的单层决策树

Parameters:
    dataArr - 数据矩阵
    classLabels - 数据标签
    D - 样本权重,每个样本权重相等 1/n
    
Returns:
    bestStump - 最佳单层决策树信息
    minError - 最小误差
"""
def buildStump(dataArr, classLabels, D):
    # 输入数据转为矩阵(5, 2)
    dataMatrix = np.mat(dataArr)
    # 将标签矩阵进行转置(5, 1)
    labelMat = np.mat(classLabels).T
    # m=5, n=2
    m, n = np.shape(dataMatrix)
    numSteps = 10.0
    bestStump = {
   }
    # (5, 1)全零列矩阵
    bestClasEst = np.mat(np.zeros((m, 1)))
    # 最小误差初始化为正无穷大inf
    minError = float('inf')
    # 遍历所有特征
    for i in range(n):
        # 找到(每列)特征中的最小值和最大值
        rangeMin = dataMatrix[:, i].min()
        rangeMax = dataMatrix[:, i].max()
        # 计算步长
        stepSize = (rangeMax - rangeMin) / numSteps
        for j in range(-1, int(numSteps) + 1):
            # 大于和小于的情况均遍历，lt:Less than  gt:greater than
            for inequal in ['lt', 'gt']:
                # 计算阈值
                threshVal = (rangeMin + float(j) * stepSize)
                # 计算分类结果
                predictedVals = stumpClassify(dataMatrix, i, threshVal, inequal)
                # 初始化误差矩阵
                errArr = np.mat(np.ones((m, 1)))
                # 分类正确的，赋值为0
                errArr[predictedVals == labelMat] = 0
                # 计算误差
                weightedError = D.T * errArr
                print("split: dim %d, thresh %.2f, thresh ineqal: %s, the weighted error is %.3f" % (i, threshVal, inequal, weightedError))
                # 找到误差最小的分类方式
                if weightedError < minError:
                    minError = weightedError
                    bestClasEst = predictedVals.copy()
                    bestStump['dim'] = i
                    bestStump['thresh'] = threshVal
                    bestStump['ineq'] = inequal
    return bestStump, minError, bestClasEst


"""
Desc:
    使用AdaBoost进行优化

Parameters:
    dataArr - 数据矩阵
    classLabels - 数据标签
    numIt - 最大迭代次数
    
Returns:
    weakClassArr - 存储单层决策树的list
    aggClassEsc - 训练的label
"""
def adaBoostTrainDS(dataArr, classLabels, numIt=40):
    weakClassArr = []
    # 获取数据集的行数
    m = np.shape(dataArr)[0]
    # 样本权重，每个样本权重相等，即1/n
    D = np.mat(np.ones((m, 1)) / m)
    # 初始化为全零列
    aggClassEst = np.mat(np.zeros((m, 1)))
    # 迭代
    for i in range(numIt):
        # 构建单层决策树
        bestStump, error, classEst = buildStump(dataArr, classLabels, D)
        # print("D:", D.T)
        # 计算弱学习算法权重alpha，使error不等于0，因为分母不能为0
        alpha = float(0.5 * np.log((1.0 - error) / max(error, 1e-16)))
        # 存储弱学习算法权重
        bestStump['alpha'] = alpha
        # 存储单层决策树
        weakClassArr.append(bestStump)
        # 打印最佳分类结果
        # print("classEst: ", classEst.T)
        # 计算e的指数项
        expon = np.multiply(-1 * alpha * np.mat(classLabels).T, classEst)
        # 计算递推公式的分子
        D = np.multiply(D, np.exp(expon))
        # 根据样本权重公式，更新样本权重
        D = D / D.sum()
        # 计算AdaBoost误差，当误差为0的时候，退出循环
        # 以下为错误率累计计算
        aggClassEst += alpha * classEst
        # print("aggClassEst: ", aggClassEst.T)
        # 计算误差
        aggErrors = np.multiply(np.sign(aggClassEst) != np.mat(classLabels).T, np.ones((m, 1)))
        errorRate = aggErrors