實驗四 決策樹演算法及應用

一、實驗目的

理解決策樹演算法原理，掌握決策樹演算法框架；
理解決策樹學習演算法的特徵選擇、樹的生成和樹的剪枝；
能根據不同的資料型別，選擇不同的決策樹演算法；
針對特定應用場景及資料，能應用決策樹演算法解決實際問題。

二、實驗內容

設計演算法實現熵、經驗條件熵、資訊增益等方法。
實現ID3演算法。
熟悉sklearn庫中的決策樹演算法；
針對iris資料集，應用sklearn的決策樹演算法進行類別預測。
針對iris資料集，利用自編決策樹演算法進行類別預測。

三、實驗報告要求

對照實驗內容，撰寫實驗過程、演算法及測試結果；
程式碼規範化：命名規則、註釋；
分析核心演算法的複雜度；
查閱文獻，討論ID3、5演算法的應用場景；
查詢文獻，分析決策樹剪枝策略。

四、實驗程式碼

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from collections import Counter
import math
from math import log
import pprint

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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'年齡', u'有工作', u'有自己的房子', u'信貸情況', u'類別']
    # 返回資料集和每個維度的名稱
    return datasets, labels
 

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datasets, labels = create_data()

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

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train_data

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# 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
# def entropy(y):
# """
# Entropy of a label sequence
# """
# hist = np.bincount(y)
# ps = hist / np.sum(hist)
# return -np.sum([p * np.log2(p) for p in ps if p > 0])
# 經驗條件熵
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
# 資訊增益
def info_gain(ent, cond_ent):
    return ent - cond_ent
def info_gain_train(datasets):
    count = len(datasets[0]) - 1
    ent = calc_ent(datasets)
# ent = entropy(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('特徵({}) - info_gain - {:.3f}'.format(labels[c], c_info_gain))
# 比較大小
    best_ = max(best_feature, key=lambda x: x[-1])
    return '特徵({})的資訊增益最大，選擇為根節點特徵'.format(labels[best_[0]])

 

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info_gain_train(np.array(datasets))

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# 定義節點類 二叉樹
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
    # 經驗條件熵
    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
    # 資訊增益
    @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))
        # 比較大小
        best_ = max(best_feature, key=lambda x: x[-1])
        return best_
    def train(self, train_data):
        """
        input:資料集D(DataFrame格式)，特徵集A，閾值eta
        output:決策樹T
        """
        _, y_train, features = train_data.iloc[:, :
                                                -1], train_data.iloc[:,
                                                                    -1], train_data.columns[:
                                                                                            -1]
        # 1,若D中例項屬於同一類Ck，則T為單節點樹，並將類Ck作為結點的類標記，返回T
        if len(y_train.value_counts()) == 1:
            return Node(root=True, label=y_train.iloc[0])
        # 2, 若A為空，則T為單節點樹，將D中例項樹最大的類Ck作為該節點的類標記，返回T
        if len(features) == 0:
            return Node(
                root=True,
                label=y_train.value_counts().sort_values(
                    ascending=False).index[0])
        # 3,計算最大資訊增益 同5.1,Ag為資訊增益最大的特徵
        max_feature, max_info_gain = self.info_gain_train(np.array(train_data))
        max_feature_name = features[max_feature]
        # 4,Ag的資訊增益小於閾值eta,則置T為單節點樹，並將D中是例項數最大的類Ck作為該節點的類標記，返
        if max_info_gain < self.epsilon:
            return Node(
                root=True,
                label=y_train.value_counts().sort_values(
                    ascending=False).index[0])
        # 5,構建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, 遞迴生成樹
            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)

9

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

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tree

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dt.predict(['老年', '否', '否', '一般'])

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# data
def 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)

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from sklearn.tree import DecisionTreeClassifier
from sklearn.tree import export_graphviz
import graphviz

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

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clf.score(X_test, y_test)

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

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graphviz.Source(dot_graph)

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from sklearn.tree import DecisionTreeClassifier
from sklearn import preprocessing
import numpy as np
import pandas as pd
from sklearn import tree
import graphviz
features = ["年齡", "有工作", "有自己的房子", "信貸情況"]
X_train = pd.DataFrame([
    ["青年", "否", "否", "一般"],
    ["青年", "否", "否", "好"],
    ["青年", "是", "否", "好"],
    ["青年", "是", "是", "一般"],
    ["青年", "否", "否", "一般"],
    ["中年", "否", "否", "一般"],
    ["中年", "否", "否", "好"],
    ["中年", "是", "是", "好"],
    ["中年", "否", "是", "非常好"],
    ["中年", "否", "是", "非常好"],
    ["老年", "否", "是", "非常好"],
    ["老年", "否", "是", "好"],
    ["老年", "是", "否", "好"],
    ["老年", "是", "否", "非常好"],
    ["老年", "否", "否", "一般"]
])
y_train = pd.DataFrame(["否", "否", "是", "是", "否",
                        "否", "否", "是", "是", "是",
                        "是", "是", "是", "是", "否"])
# 資料預處理
le_x = preprocessing.LabelEncoder()
le_x.fit(np.unique(X_train))
X_train = X_train.apply(le_x.transform)
le_y = preprocessing.LabelEncoder()
le_y.fit(np.unique(y_train))
y_train = y_train.apply(le_y.transform)
# 呼叫sklearn.DT建立訓練模型
model_tree = DecisionTreeClassifier()
model_tree.fit(X_train, y_train)
# 視覺化
dot_data = tree.export_graphviz(model_tree, out_file=None,
                                    feature_names=features,
                                    class_names=[str(k) for k in np.unique(y_train)],
                                    filled=True, rounded=True,
                                    special_characters=True)
graph = graphviz.Source(dot_data)
graph

19

import numpy as np
class LeastSqRTree:
    def __init__(self, train_X, y, epsilon):
        # 訓練集特徵值
        self.x = train_X
        # 類別
        self.y = y
        # 特徵總數
        self.feature_count = train_X.shape[1]
        # 損失閾值
        self.epsilon = epsilon
        # 迴歸樹
        self.tree = None
    def _fit(self, x, y, feature_count, epsilon):
        # 選擇最優切分點變數j與切分點s
        (j, s, minval, c1, c2) = self._divide(x, y, feature_count)
        # 初始化樹
        tree = {"feature": j, "value": x[s, j], "left": None, "right": None}
        if minval < self.epsilon or len(y[np.where(x[:, j] <= x[s, j])]) <= 1:
            tree["left"] = c1
        else:
            tree["left"] = self._fit(x[np.where(x[:, j] <= x[s, j])],
                                     y[np.where(x[:, j] <= x[s, j])],
                                     self.feature_count, self.epsilon)
        if minval < self.epsilon or len(y[np.where(x[:, j] > s)]) <= 1:
            tree["right"] = c2
        else:
            tree["right"] = self._fit(x[np.where(x[:, j] > x[s, j])],
                                      y[np.where(x[:, j] > x[s, j])],
                                      self.feature_count, self.epsilon)
        return tree
    def fit(self):
        self.tree = self._fit(self.x, self.y, self.feature_count, self.epsilon)
    @staticmethod
    def _divide(x, y, feature_count):
        # 初始化損失誤差
        cost = np.zeros((feature_count, len(x)))
        # 公式5.21
        for i in range(feature_count):
            for k in range(len(x)):
                # k行i列的特徵值
                value = x[k, i]
                y1 = y[np.where(x[:, i] <= value)]
                c1 = np.mean(y1)
                y2 = y[np.where(x[:, i] > value)]
                c2 = np.mean(y2)
                y1[:] = y1[:] - c1
                y2[:] = y2[:] - c2
                cost[i, k] = np.sum(y1 * y1) + np.sum(y2 * y2)
        # 選取最優損失誤差點
        cost_index = np.where(cost == np.min(cost))
        # 選取第幾個特徵值
        j = cost_index[0][0]
        # 選取特徵值的切分點
        s = cost_index[1][0]
        # 求兩個區域的均值c1,c2
        c1 = np.mean(y[np.where(x[:, j] <= x[s, j])])
        c2 = np.mean(y[np.where(x[:, j] > x[s, j])])
        return j, s, cost[cost_index], c1, c2

20

train_X = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]).T
y = np.array([4.50, 4.75, 4.91, 5.34, 5.80, 7.05, 7.90, 8.23, 8.70, 9.00])
model_tree = LeastSqRTree(train_X, y, .2)
model_tree.fit()
model_tree.tree

五、執行截圖

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五、實驗小結

通過這次試驗，我理解了決策樹的演算法原理，決策樹演算法是一種逼近離散函式值的方法。它是一種典型的分類方法，首先對資料進行處理，利用歸納演算法生成可讀的規則和決策樹，然後使用決策對新資料進行分析。本質上決策樹是通過一系列規則對資料進行分類的過程。