数据挖掘算法原理与实践：决策树

感谢阳博导远程指导

第二关：决策树算法原理

#encoding=utf8
import numpy as np

# 计算熵
def calcInfoEntropy(label):
    '''
    input:
        label(narray):样本标签
    output:
        InfoEntropy(float):熵
    '''
    #********* Begin *********#
    label_set = set(label)
    InfoEntropy = 0
    
    for temp_label in label_set:
        count = 0
        for j in range(len(label)):
            if label[j] == temp_label:
                count += 1
        # 计算标签在数据集中出现的概率
        p = count / len(label)
        # 计算熵
        InfoEntropy -= p * np.log2(p)

    #********* End *********#
    return InfoEntropy

#计算条件熵
def calcHDA(feature,label,index,value):
    '''
    input:
        feature(ndarray):样本特征
        label(ndarray):样本标签
        index(int):需要使用的特征列索引
        value(int):index所表示的特征列中需要考察的特征值
    output:
        HDA(float):信息熵
    '''
    #********* Begin *********#
    count = 0
    # sub_feature和sub_label表示根据特征列和特征值分割出的子数据集中的特征和标签
    sub_feature = []
    sub_label = []
    for i in range(len(feature)):
        if feature[i][index] == value:
            count += 1
            sub_feature.append(feature[i])
            sub_label.append(label[i])
    pHA = count / len(feature)
    e = calcInfoEntropy(sub_label)
    HDA =  pHA * e
    #********* End *********#
    return HDA

#计算信息增益
def calcInfoGain(feature, label, index):
    '''
    input:
        feature(ndarry):测试用例中字典里的feature
        label(ndarray):测试用例中字典里的label
        index(int):测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
    output:
        InfoGain(float):信息增益
    '''
    #********* Begin *********#
    # 得到指定特征列的值的集合
    base_e = calcInfoEntropy(label)
    f = np.array(feature)
    # 计算条件熵
    f_set = set(f[:, index])
    sum_HDA = 0
    # 计算信息增益
    for value in f_set:
        sum_HDA += calcHDA(feature, label, index, value)
    InfoGain =  base_e - sum_HDA
    #********* End *********#
    return InfoGain

第三关：动手实现ID3决策树

import numpy as np

# 计算熵
def calcInfoEntropy(label):
    '''
    input:
        label(narray):样本标签
    output:
        InfoEntropy(float):熵
    '''
    label_set = set(label)
    InfoEntropy = 0
    for l in label_set:
        count = 0
        for j in range(len(label)):
            if label[j] == l:
                count += 1
        # 计算标签在数据集中出现的概率
        p = count / len(label)
        # 计算熵
        InfoEntropy -= p * np.log2(p)
    return InfoEntropy

#计算条件熵
def calcHDA(feature,label,index,value):
    '''
    input:
        feature(ndarray):样本特征
        label(ndarray):样本标签
        index(int):需要使用的特征列索引
        value(int):index所表示的特征列中需要考察的特征值
    output:
        HDA(float):信息熵
    '''
    count = 0
    # sub_feature和sub_label表示根据特征列和特征值分割出的子数据集中的特征和标签
    sub_feature = []
    sub_label = []
    for i in range(len(feature)):
        if feature[i][index] == value:
            count += 1
            sub_feature.append(feature[i])
            sub_label.append(label[i])
    pHA = count / len(feature)
    e = calcInfoEntropy(sub_label)
    HDA = pHA * e
    return HDA

#计算信息增益
def calcInfoGain(feature, label, index):
    '''
    input:
        feature(ndarry):测试用例中字典里的feature
        label(ndarray):测试用例中字典里的label
        index(int):测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
    output:
        InfoGain(float):信息增益
    '''
    base_e = calcInfoEntropy(label)
    f = np.array(feature)
    # 得到指定特征列的值的集合
    f_set = set(f[:, index])
    sum_HDA = 0
    # 计算条件熵
    for value in f_set:
        sum_HDA += calcHDA(feature, label, index, value)
    # 计算信息增益
    InfoGain = base_e - sum_HDA
    return InfoGain

# 获得信息增益最高的特征
def getBestFeature(feature, label):
    '''
    input:
        feature(ndarray):样本特征
        label(ndarray):样本标签
    output:
        best_feature(int):信息增益最高的特征
    '''
    #*********Begin*********#
    max_infogain = 0
    best_feature = 0
    for i in range(len(feature[0])):
        infogain = calcInfoGain(feature, label, i)
        if infogain > max_infogain:
            max_infogain = infogain
            best_feature = i
    #*********End*********#
    return best_feature

#创建决策树
def createTree(feature, label):
    '''
    input:
        feature(ndarray):训练样本特征
        label(ndarray):训练样本标签
    output:
        tree(dict):决策树模型    
    '''
    #*********Begin*********#
    # 样本里都是同一个label没必要继续分叉了
    if len(set(label)) == 1:
        return label[0]
    # 样本中只有一个特征或者所有样本的特征都一样的话就看哪个label的票数高
    if len(feature[0]) == 1 or len(np.unique(feature, axis=0)) == 1:
        vote = {}
        for l in label:
            if l in vote.keys():
                vote[l] += 1
            else:
                vote[l] = 1
        max_count = 0
        vote_label = None
        for k, v in vote.items():
            if v > max_count:
                max_count = v
                vote_label = k
        return vote_label

    # 根据信息增益拿到特征的索引
    best_feature = getBestFeature(feature, label)
    tree = {best_feature: {}}
    f = np.array(feature)
    # 拿到bestfeature的所有特征值
    f_set = set(f[:, best_feature])
    # 构建对应特征值的子样本集sub_feature, sub_label
    for v in f_set:
        sub_feature = []
        sub_label = []
        for i in range(len(feature)):
            if feature[i][best_feature] == v:
                sub_feature.append(feature[i])
                sub_label.append(label[i])
        # 递归构建决策树
        tree[best_feature][v] = createTree(sub_feature, sub_label)
    #*********End*********#
    return tree

#决策树分类
def dt_clf(train_feature,train_label,test_feature):
    '''
    input:
        train_feature(ndarray):训练样本特征
        train_label(ndarray):训练样本标签
        test_feature(ndarray):测试样本特征
    output:
        predict(ndarray):测试样本预测标签     
    '''
    #*********Begin*********#
    result = []
    tree = createTree(train_feature,train_label)

    def classify(tree, feature):
        if not isinstance(tree, dict):
            return tree
        t_index, t_value = list(tree.items())[0]
        f_value = feature[t_index]
        if isinstance(t_value, dict):
            classLabel = classify(tree[t_index][f_value], feature)
            return classLabel
        else:
            return t_value

    for feature in test_feature:
        result.append(classify(tree, feature))

    predict = np.array(result)
    #*********End*********#
    return predict