“机器学习”系列之决策树

import numpy as npimport pandas as pdimport matplotlib.pyplot as plt
%matplotlib inlinefrom sklearn.datasets import load_irisfrom sklearn.model_selection import train_test_splitfrom collections import Counterimport mathfrom math import logimport pprint

def create_data():
    datasets = [['青年', '否', '否', '一般', '否'],
               ['青年', '否', '否', '好', '否'],
               ['青年', '是', '否', '好', '是'],
               ['青年', '是', '是', '一般', '是'],
               ['青年', '否', '否', '一般', '否'],
               ['中年', '否', '否', '一般', '否'],
               ['中年', '否', '否', '好', '否'],
               ['中年', '是', '是', '好', '是'],
               ['中年', '否', '是', '非常好', '是'],
               ['中年', '否', '是', '非常好', '是'],
               ['老年', '否', '是', '非常好', '是'],
               ['老年', '否', '是', '好', '是'],
               ['老年', '是', '否', '好', '是'],
               ['老年', '是', '否', '非常好', '是'],
               ['老年', '否', '否', '一般', '否'],
               ]
    labels = [u'年龄', u'有工作', u'有自己的房子', u'信贷情况', u'类别']    # 返回数据集和每个维度的名称
    return datasets, labels

datasets, labels = create_data()

train_data = pd.DataFrame(datasets, columns=labels)

train_data

# 熵def calc_ent(datasets):
    data_length = len(datasets)
    label_count = {}    for i in range(data_length):
        label = datasets[i][-1]        if label not in label_count:
            label_count[label] = 0
        label_count[label] += 1
    ent = -sum([(p/data_length)*log(p/data_length, 2) for p in label_count.values()])    return ent# 经验条件熵def cond_ent(datasets, axis=0):
    data_length = len(datasets)
    feature_sets = {}    for i in range(data_length):
        feature = datasets[i][axis]        if feature not in feature_sets:
            feature_sets[feature] = []
        feature_sets[feature].append(datasets[i])
    cond_ent = sum([(len(p)/data_length)*calc_ent(p) for p in feature_sets.values()])    return cond_ent# 信息增益def info_gain(ent, cond_ent):
    return ent - cond_entdef info_gain_train(datasets):
    count = len(datasets[0]) - 1
    ent = calc_ent(datasets)
    best_feature = []    for c in range(count):
        c_info_gain = info_gain(ent, cond_ent(datasets, axis=c))
        best_feature.append((c, c_info_gain))        print('特征({}) - info_gain - {:.3f}'.format(labels[c], c_info_gain))    # 比较大小
    best_ = max(best_feature, key=lambda x: x[-1])    return '特征({})的信息增益最大，选择为根节点特征'.format(labels[best_[0]])

info_gain_train(np.array(datasets))

# 定义节点类 二叉树class Node:
    def __init__(self, root=True, label=None, feature_name=None, feature=None):
        self.root = root
        self.label = label
        self.feature_name = feature_name
        self.feature = feature
        self.tree = {}
        self.result = {'label:': self.label, 'feature': self.feature, 'tree': self.tree}    def __repr__(self):
        return '{}'.format(self.result)    def add_node(self, val, node):
        self.tree[val] = node    def predict(self, features):
        if self.root is True:            return self.label        return self.tree[features[self.feature]].predict(features)    
class DTree:
    def __init__(self, epsilon=0.1):
        self.epsilon = epsilon
        self._tree = {}    # 熵    @staticmethod
    def calc_ent(datasets):
        data_length = len(datasets)
        label_count = {}        for i in range(data_length):
            label = datasets[i][-1]            if label not in label_count:
                label_count[label] = 0
            label_count[label] += 1
        ent = -sum([(p/data_length)*log(p/data_length, 2) for p in label_count.values()])        return ent    # 经验条件熵
    def cond_ent(self, datasets, axis=0):
        data_length = len(datasets)
        feature_sets = {}        for i in range(data_length):
            feature = datasets[i][axis]            if feature not in feature_sets:
                feature_sets[feature] = []
            feature_sets[feature].append(datasets[i])
        cond_ent = sum([(len(p)/data_length)*self.calc_ent(p) for p in feature_sets.values()])        return cond_ent    # 信息增益    @staticmethod
    def info_gain(ent, cond_ent):
        return ent - cond_ent    def info_gain_train(self, datasets):
        count = len(datasets[0]) - 1
        ent = self.calc_ent(datasets)
        best_feature = []        for c in range(count):
            c_info_gain = self.info_gain(ent, self.cond_ent(datasets, axis=c))
            best_feature.append((c, c_info_gain))        # 比较大小
        best_ = max(best_feature, key=lambda x: x[-1])        return best_    def train(self, train_data):
        """
        input:数据集D(DataFrame格式)，特征集A，阈值eta
        output:决策树T
        """
        _, y_train, features = train_data.iloc[:, :-1], train_data.iloc[:, -1], train_data.columns[:-1]        # 1,若D中实例属于同一类Ck，则T为单节点树，并将类Ck作为结点的类标记，返回T
        if len(y_train.value_counts()) == 1:            return Node(root=True,
                        label=y_train.iloc[0])        # 2, 若A为空，则T为单节点树，将D中实例树最大的类Ck作为该节点的类标记，返回T
        if len(features) == 0:            return Node(root=True, label=y_train.value_counts().sort_values(ascending=False).index[0])        # 3,计算最大信息增益 同5.1,Ag为信息增益最大的特征
        max_feature, max_info_gain = self.info_gain_train(np.array(train_data))
        max_feature_name = features[max_feature]        # 4,Ag的信息增益小于阈值eta,则置T为单节点树，并将D中是实例数最大的类Ck作为该节点的类标记，返回T
        if max_info_gain < self.epsilon:            return Node(root=True, label=y_train.value_counts().sort_values(ascending=False).index[0])        # 5,构建Ag子集
        node_tree = Node(root=False, feature_name=max_feature_name, feature=max_feature)

        feature_list = train_data[max_feature_name].value_counts().index        for f in feature_list:
            sub_train_df = train_data.loc[train_data[max_feature_name] == f].drop([max_feature_name], axis=1)            # 6, 递归生成树
            sub_tree = self.train(sub_train_df)
            node_tree.add_node(f, sub_tree)        # pprint.pprint(node_tree.tree)
        return node_tree    def fit(self, train_data):
        self._tree = self.train(train_data)        return self._tree    def predict(self, X_test):
        return self._tree.predict(X_test)

datasets, labels = create_data()
data_df = pd.DataFrame(datasets, columns=labels)
dt = DTree()
tree = dt.fit(data_df)

tree

dt.predict(['老年', '否', '否', '一般'])

# datadef create_data():
    iris = load_iris()
    df = pd.DataFrame(iris.data, columns=iris.feature_names)
    df['label'] = iris.target
    df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
    data = np.array(df.iloc[:100, [0, 1, -1]])    # print(data)
    return data[:,:2], data[:,-1]

X, y = create_data()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

from sklearn.tree import DecisionTreeClassifierfrom sklearn.tree import export_graphvizimport graphviz

clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)

clf.score(X_test, y_test)

tree_pic = export_graphviz(clf, out_file="mytree.pdf")with open('mytree.pdf') as f:
    dot_graph = f.read()

# 决策树可视化graphviz.Source(dot_graph)