sklearn决策树特征权重计算方法

训练模型，生成树图

from io import StringIO
from sklearn.datasets import load_iris
from sklearn.tree import DecisionTreeClassifier
from sklearn import tree
import pydot

for criterion in ['gini', 'entropy']:
    clf = DecisionTreeClassifier(criterion=criterion, random_state=0, max_depth=3)
    iris = load_iris()

    dot_data = StringIO()

    clf.fit(iris.data, iris.target)
    print(clf.feature_importances_)
    tree.export_graphviz(clf, out_file=dot_data)
    graph = pydot.graph_from_dot_data(dot_data.getvalue())
    graph[0].write_png('iris_%s.png' % criterion)

# [ 0.          0.          0.05393633  0.94606367]  gini
# [ 0.          0.          0.07060267  0.92939733]  entropy

gini 

entropy

计算 importance，比较和模型生成权重的一致性

import numpy as np

def split_gain(gini, n, gini1, n1, gini2, n2, t):
    return (n*gini - n1*gini1 - n2*gini2)*1.0/t

# gini

x3_gain = 
    split_gain(0.6667, 150, 0, 50, 0.5, 100, 150) + 
    split_gain(0.5, 100, 0.168, 54, 0.0425, 46, 150)

x2_gain = 
    split_gain(0.168, 54, 0.0408, 48, 0.4444, 6, 150) + 
    split_gain(0.0425, 46, 0.4444, 3, 0, 43, 150)

x = np.array([x2_gain, x3_gain])
x = x / np.sum(x)
print('gini:', x)

# [ 0.05389858  0.94610142] computed
# [ 0.05393633  0.94606367] sklearn

x3_gain = 
    split_gain(1.585, 150, 0, 50, 1, 100, 150) + 
    split_gain(1, 100, 0.4451, 54, 0.1511, 46, 150)

x2_gain = 
    split_gain(0.4451, 54, 0.1461, 48, 0.9183, 6, 150) + 
    split_gain(0.1511, 46, 0.9183, 3, 0, 43, 150)

x = np.array([x2_gain, x3_gain])
x = x / np.sum(x)
print('entropy:', x)
# [ 0.07060873  0.92939127] computed
# [ 0.07060267  0.92939733] sklearn

总结

计算特征    对不存度减少的贡献，同时考虑 节点的样本量

对于某节点计算（**criterion可为gini或entropy**）

父节点  有样本量$n_0$，criterion为${c}_0$

子节点1有样本量$n_1$，criterion为${c}_1$

子节点2有样本量$n_2$，criterion为${c}_2$

总样本个数为$T$

$gain = left(n_0*{c}_0 -n_1*{c}_1-n_2*{c}_2  ight)/T$