一、熵

公式：
$−∑i=1np(xi)∗log2p(xi)-\sum_{i = 1}^{n}{p(xi)*log_2p(xi)}$

$∑i=1np(xi)∗log21p(xi)\sum_{i=1}^{n}p(xi)*log_2\frac{1}{p(xi)}$

在这里插入图片描述

import numpy as np# 账号是否真实：3no（0.3） 7yes（0.7）# 不进行划分，信息熵
info_D = 0.3*np.log2(1/0.3) + 0.7*np.log2(1/0.7)
info_D

0.8812908992306926

# 决策树，对目标值进行划分
# 三个属性：日志密度，好友密度，是否真实头像
# 使用日志密度进行树构建
# 3 s 0.3 -------> 2no 1yes
# 4 m 0.4 -------> 1no 3yes
# 3 l 0.3 -------> 3yesinfo_L_D = 0.3*(2/3*np.log2(3/2) + 1/3*np.log2(3)) + 0.4 * (0.25*np.log2(4) + 0.75*np.log2(4/3)) + 0.3*(1*np.log2(1))
info_L_D

0.5999999999999999

# 信息增益
info_D - info_L_D

0.2812908992306927

# 好友密度
# 4 s 0.4 ---> 3no 1yes
# 4 m 0.4 ---> 4yes
# 2 l 0.2 ---> 2yes
info_F_D = 0.4*(0.75*np.log2(4/3) + 0.25*np.log2(4)) + 0 + 0
info_F_D

0.32451124978365314

# 信息增益
info_D - info_F_D

0.5567796494470394

二、决策树

1导包

from sklearn import datasets import numpy as npfrom sklearn.tree import DecisionTreeClassifierfrom sklearn import datasetsimport matplotlib.pyplot as plt
%matplotlib inlinefrom sklearn import treefrom sklearn.model_selection import train_test_split

2取数据

X,y = datasets.load_iris(True)
X 
iris = datasets.load_iris()X = iris['data']y = iris['target']feature_names = iris.feature_names
X_train,X_test,y_train,y_test = train_test_split(X,y,test_size = 0.2,random_state  = 1024)

3决策树的使用

# 数据清洗，花时间# 特征工程# 使用模型进行训练# 模型参数调优# sklearn所有算法，封装好了
# 直接用，使用规则如下clf = DecisionTreeClassifier(criterion='entropy')clf.fit(X_train,y_train)y_ = clf.predict(X_test)from sklearn.metrics import accuracy_scoreaccuracy_score(y_test,y_)

1.0

39/120*np.log2(120/39) + 42/120*np.log2(120/42) + 39/120*np.log2(120/39)

1.5840680553754911

42/81*np.log2(81/42) + 39/81*np.log2(81/39)

0.9990102708804813

plt.figure(figsize=(18,12))
_ = tree.plot_tree(clf,filled = True,feature_names=feature_names,max_depth=1)
plt.savefig('./tree.jpg') 
# 连续的，continuous 属性 阈值 threshold
X_train 
# 波动程度，越大，离散，越容易分开
X_train.std(axis = 0)

array([0.82300095, 0.42470578, 1.74587112, 0.75016619])

1.9 + 3.3 = 5.25.2/2 = 2.6

np.sort(X_train[:,2])

%%time
# 树的深度变浅了，树的裁剪
clf = DecisionTreeClassifier(criterion='entropy',max_depth=5)clf.fit(X_train,y_train)y_ = clf.predict(X_test)from sklearn.metrics import accuracy_scoreprint(accuracy_score(y_test,y_))plt.figure(figsize=(18,12))_ = tree.plot_tree(clf,filled=True,feature_names = feature_names)

1.0
Wall time: 114 ms

%%time
# 树的深度变浅了，树的裁剪
clf = DecisionTreeClassifier(criterion='gini',max_depth=5)clf.fit(X_train,y_train)y_ = clf.predict(X_test)from sklearn.metrics import accuracy_scoreprint(accuracy_score(y_test,y_))plt.figure(figsize=(18,12))_ = tree.plot_tree(clf,filled=True,feature_names = feature_names)

1.0
Wall time: 113 ms
在这里插入图片描述

gini 系数公式：

$∑i=0np(xi)∗(1−p(xi))\sum_{i = 0}^{n}p(xi)*(1-p(xi))$

# 1.0 其余都是0
# 百分之百纯
gini = 1*(1-1)
gini

# 39 42 39
39/120*(1 - 39/120)*2 + 42/120*(1 - 42/120)

0.66625

feature_names

['sepal length (cm)','sepal width (cm)','petal length (cm)','petal width (cm)']

X_train2 = X_train[y_train != 0]
X_train2y_train2 = y_train[y_train!=0]
y_train2index = np.argsort(X_train2[:,0])display(X_train2[:,0][index])y_train2[index]```python
index = np.argsort(X_train2[:,1])display(X_train2[:,1][index])y_train2[index] 
index = np.argsort(X_train2[:,2])display(X_train2[:,2][index])y_train2[index] 
index = np.argsort(X_train2[:,3])display(X_train2[:,3][index])y_train2[index]

决策树模型，不需要对数据进行去量纲化，规划化，标准化

公司应用中，不用决策树，太简单

决策树升级版：集成算法（随机森林，（extrem）极限森林，梯度提升树，adaboost提升树）

三、随机森林

import numpy as npimport matplotlib.pyplot as plt
%matplotlib inlinefrom sklearn.ensemble import RandomForestClassifier,ExtraTreesClassifierfrom sklearn import datasetsimport pandas as pdfrom sklearn.model_selection import train_test_splitfrom sklearn.tree import DecisionTreeClassifierfrom sklearn.metrics import accuracy_score

随机森林：多颗决策树构建而成，每一颗决策树都是刚才讲到的决策树原理
多颗决策树一起运算------------>集成算法
~~随机森林，随机什么意思~~

wine = datasets.load_wine()
wine

{'data': array([[1.423e+01, 1.710e+00, 2.430e+00, ..., 1.040e+00, 3.920e+00,1.065e+03],[1.320e+01, 1.780e+00, 2.140e+00, ..., 1.050e+00, 3.400e+00,1.050e+03],[1.316e+01, 2.360e+00, 2.670e+00, ..., 1.030e+00, 3.170e+00,1.185e+03],...,[1.327e+01, 4.280e+00, 2.260e+00, ..., 5.900e-01, 1.560e+00,8.350e+02],[1.317e+01, 2.590e+00, 2.370e+00, ..., 6.000e-01, 1.620e+00,8.400e+02],[1.413e+01, 4.100e+00, 2.740e+00, ..., 6.100e-01, 1.600e+00,5.600e+02]]),'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2, 2]),'target_names': array(['class_0', 'class_1', 'class_2'], dtype='<U7'),'DESCR': '.. _wine_dataset:\n\nWine recognition dataset\n------------------------\n\n**Data Set Characteristics:**\n\n    :Number of Instances: 178 (50 in each of three classes)\n    :Number of Attributes: 13 numeric, predictive attributes and the class\n    :Attribute Information:\n \t\t- Alcohol\n \t\t- Malic acid\n \t\t- Ash\n\t\t- Alcalinity of ash  \n \t\t- Magnesium\n\t\t- Total phenols\n \t\t- Flavanoids\n \t\t- Nonflavanoid phenols\n \t\t- Proanthocyanins\n\t\t- Color intensity\n \t\t- Hue\n \t\t- OD280/OD315 of diluted wines\n \t\t- Proline\n\n    - class:\n            - class_0\n            - class_1\n            - class_2\n\t\t\n    :Summary Statistics:\n    \n    ============================= ==== ===== ======= =====\n                                   Min   Max   Mean     SD\n    ============================= ==== ===== ======= =====\n    Alcohol:                      11.0  14.8    13.0   0.8\n    Malic Acid:                   0.74  5.80    2.34  1.12\n    Ash:                          1.36  3.23    2.36  0.27\n    Alcalinity of Ash:            10.6  30.0    19.5   3.3\n    Magnesium:                    70.0 162.0    99.7  14.3\n    Total Phenols:                0.98  3.88    2.29  0.63\n    Flavanoids:                   0.34  5.08    2.03  1.00\n    Nonflavanoid Phenols:         0.13  0.66    0.36  0.12\n    Proanthocyanins:              0.41  3.58    1.59  0.57\n    Colour Intensity:              1.3  13.0     5.1   2.3\n    Hue:                          0.48  1.71    0.96  0.23\n    OD280/OD315 of diluted wines: 1.27  4.00    2.61  0.71\n    Proline:                       278  1680     746   315\n    ============================= ==== ===== ======= =====\n\n    :Missing Attribute Values: None\n    :Class Distribution: class_0 (59), class_1 (71), class_2 (48)\n    :Creator: R.A. Fisher\n    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n    :Date: July, 1988\n\nThis is a copy of UCI ML Wine recognition datasets.\nhttps://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\n\nThe data is the results of a chemical analysis of wines grown in the same\nregion in Italy by three different cultivators. There are thirteen different\nmeasurements taken for different constituents found in the three types of\nwine.\n\nOriginal Owners: \n\nForina, M. et al, PARVUS - \nAn Extendible Package for Data Exploration, Classification and Correlation. \nInstitute of Pharmaceutical and Food Analysis and Technologies,\nVia Brigata Salerno, 16147 Genoa, Italy.\n\nCitation:\n\nLichman, M. (2013). UCI Machine Learning Repository\n[https://archive.ics.uci.edu/ml]. Irvine, CA: University of California,\nSchool of Information and Computer Science. \n\n.. topic:: References\n\n  (1) S. Aeberhard, D. Coomans and O. de Vel, \n  Comparison of Classifiers in High Dimensional Settings, \n  Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of  \n  Mathematics and Statistics, James Cook University of North Queensland. \n  (Also submitted to Technometrics). \n\n  The data was used with many others for comparing various \n  classifiers. The classes are separable, though only RDA \n  has achieved 100% correct classification. \n  (RDA : 100%, QDA 99.4%, LDA 98.9%, 1NN 96.1% (z-transformed data)) \n  (All results using the leave-one-out technique) \n\n  (2) S. Aeberhard, D. Coomans and O. de Vel, \n  "THE CLASSIFICATION PERFORMANCE OF RDA" \n  Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of \n  Mathematics and Statistics, James Cook University of North Queensland. \n  (Also submitted to Journal of Chemometrics).\n','feature_names': ['alcohol','malic_acid','ash','alcalinity_of_ash','magnesium','total_phenols','flavanoids','nonflavanoid_phenols','proanthocyanins','color_intensity','hue','od280/od315_of_diluted_wines','proline']}

X = wine['data']y = wine['target']X.shape

(178, 13)

将数据分割

X_train,X_test,y_train,y_test = train_test_split(X,y,test_size = 0.2)

使用随机森林算法训练获取预测值和准确率

clf = RandomForestClassifier()clf.fit(X_train,y_train)y_ = clf.predict(X_test)accuracy_score(y_test,y_)

1.0

dt_clf = DecisionTreeClassifier()dt_clf.fit(X_train,y_train)dt_clf.score(X_test,y_test)

0.9444444444444444

对比决策树和随机森林算法的差距

score = 0 
for i in range(100):X_train,X_test,y_train,y_test = train_test_split(X,y,test_size = 0.2)dt_clf = DecisionTreeClassifier()dt_clf.fit(X_train,y_train)score+=dt_clf.score(X_test,y_test)/100print('决策树多次运行准确率：',score)

决策树多次运行准确率： 0.909166666666666

score = 0 
for i in range(100):X_train,X_test,y_train,y_test = train_test_split(X,y,test_size = 0.2)clf = RandomForestClassifier(n_estimators=100)clf.fit(X_train,y_train)score+=clf.score(X_test,y_test)/100print('随机森林多次运行准确率：',score)