1 什么是随机森林？
随机森林就是通过集成学习的思想将多棵树集成的一种算法，它的基本单元是决策树，而它的本质属于机器学习的一大分支——集成学习（Ensemble Learning）方法。
直观角度来解释，每棵决策树都是一个分类器（假设现在针对的是分类问题），那么对于一个输入样本，N棵树会有N个分类结果。而随机森林集成了所有的分类投票结果，将投票次数最多的类别指定为最终的输出，这就是一种最简单的 Bagging 思想。
2 随机森林的特点
随机森林是一种很灵活实用的方法，它有如下几个特点：
- 在当前所有算法中，具有较好的准确率/It is unexcelled in accuracy among current algorithms；
- 能够有效地运行在大数据集上/It runs efficiently on large data bases；
- 能够处理具有高维特征的输入样本，而且不需要降维/It can handle thousands of input variables without variable deletion；
- 能够评估各个特征在分类问题上的重要性/It gives estimates of what variables are important in the classification；
- 在生成过程中，能够获取到内部生成误差的一种无偏估计/It generates an internal unbiased estimate of the generalization error as the forest building progresses；
- 对于缺省值问题也能够获得很好得结果/It has an effective method for estimating missing data and maintains accuracy when a large proportion of the data are missing
实际上，随机森林的特点不只有这六点，它就相当于机器学习领域的Leatherman（多面手），你几乎可以把任何东西扔进去，它基本上都是可供使用的。
信息、熵以及信息增益的概念
3 随机森林的相关基础知识
1：数据集种类(目标变量)越多越复杂熵越大，所以原始数据的熵最大
2：熵公式：
n代表X的n种不同的离散取值，pi代表X取值为i（i∈n）的概率，log以2或e为底的对数
3：信息增益(简单处理)：原始数据熵-目前特征的熵
决策树原理：（这里只是重点描述，决策树还是涉及很多知识的）
1：求得每个特征的熵，与目前原始数据熵比较从而得到该特征的信息增益。
2：从中选出信息增益最大的那个最优特征，将它取出来当作当前节点。
3：排除当前节点，递归继续重复1、2步骤。
4：两个条件结束3的递归。1：当前节点下目标变量唯一。 2：所有特征都循环完了。
1）从准确率上可以看出，随机森林在这三个测试集上都要优于单棵决策树，93%>85%，82%<85%，93%>90%；
2）从特征空间上直观地可以看出，随机森林比决策树拥有更强的分割能力（非线性拟合能力）。
import numpy as npimport matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_moons, make_circles, make_classification
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis as QDA
h = .02 # step size in the mesh
names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Decision Tree",
"Random Forest", "AdaBoost", "Naive Bayes", "LDA", "QDA"]
classifiers = [
KNeighborsClassifier(3),
SVC(kernel="linear", C=0.025),
SVC(gamma=2, C=1),
DecisionTreeClassifier(max_depth=5),
RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),
AdaBoostClassifier(),
GaussianNB(),
LDA(),
QDA()]
X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
random_state=1, n_clusters_per_class=1)
rng = np.random.RandomState(2)
X += 2 * rng.uniform(size=X.shape)
linearly_separable = (X, y)
datasets = [make_moons(noise=0.3, random_state=0),
make_circles(noise=0.2, factor=0.5, random_state=1),
linearly_separable
]
figure = plt.figure(figsize=(27, 9))
i = 1
# iterate over datasets
for ds in datasets:
# preprocess dataset, split into training and test part
X, y = ds
X = StandardScaler().fit_transform(X)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# just plot the dataset first
cm = plt.cm.RdBu
cm_bright = ListedColormap(['#FF0000', '#0000FF'])
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
# Plot the training points
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
# and testing points
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
i += 1
# iterate over classifiers
for name, clf in zip(names, classifiers):
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
clf.fit(X_train, y_train)
score = clf.score(X_test, y_test)
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
if hasattr(clf, "decision_function"):
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
else:
Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
# Put the result into a color plot
Z = Z.reshape(xx.shape)
ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)
# Plot also the training points
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
# and testing points
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
alpha=0.6)
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(name)
ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
size=15, horizontalalignment='right')
i += 1
figure.subplots_adjust(left=.02, right=.98)
plt.show()
