决策树是一类常见的机器学习方法，决策树学习的目的是为了产生一棵泛化能力强，即处理未见示例能力强的决策树。决策树是个递归生成的过程，如何选择最优划分属性是决策树学习的关键。我们希望决策树的分支节点所包含的样本尽可能属于同一类别，信息熵、增益率和基尼指数都可以用来形容节点的“纯度”。
以下是简单的决策树示例：
# Create a random dataset
rng = np.random.RandomState(1)
X = np.sort(5 * rng.rand(80, 1), axis=0)
y = np.sin(X).ravel()
y[::5] += 3 * (0.5 - rng.rand(16))# Fit regression model
regr_1 = DecisionTreeRegressor(max_depth=2)
regr_2 = DecisionTreeRegressor(max_depth=5)
regr_1.fit(X, y)
regr_2.fit(X, y)# Predict
X_test = np.arange(0.0, 5.0, 0.01)[:, np.newaxis]
y_1 = regr_1.predict(X_test)
y_2 = regr_2.predict(X_test)# Plot the results
plt.figure()
plt.scatter(X, y, s=20, edgecolor="black",c="darkorange", label="data")
plt.plot(X_test, y_1, color="cornflowerblue",label="max_depth=2", linewidth=2)
plt.plot(X_test, y_2, color="yellowgreen", label="max_depth=5", linewidth=2)
plt.xlabel("data")
plt.ylabel("target")
plt.title("Decision Tree Regression")
plt.legend()
plt.show()
以iris数据集为例，我们可以构建如下的决策树：
from sklearn.datasets import load_iris
from sklearn import tree
iris = load_iris()
X, y = iris.data, iris.target
clf = tree.DecisionTreeClassifier()
clf = clf.fit(X, y)tree.plot_tree(clf)
带结果图片的决策树代码
import numpy as np
import matplotlib.pyplot as pltfrom sklearn.datasets import load_iris
from sklearn.tree import DecisionTreeClassifier, plot_tree# Parameters
n_classes = 3
plot_colors = "ryb"
plot_step = 0.02# Load data
iris = load_iris()for pairidx, pair in enumerate([[0, 1], [0, 2], [0, 3],[1, 2], [1, 3], [2, 3]]):# We only take the two corresponding featuresX = iris.data[:, pair]y = iris.target# Trainclf = DecisionTreeClassifier().fit(X, y)# Plot the decision boundaryplt.subplot(2, 3, pairidx + 1)x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),np.arange(y_min, y_max, plot_step))plt.tight_layout(h_pad=0.5, w_pad=0.5, pad=2.5)Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)cs = plt.contourf(xx, yy, Z, cmap=plt.cm.RdYlBu)plt.xlabel(iris.feature_names[pair[0]])plt.ylabel(iris.feature_names[pair[1]])# Plot the training pointsfor i, color in zip(range(n_classes), plot_colors):idx = np.where(y == i)plt.scatter(X[idx, 0], X[idx, 1], c=color, label=iris.target_names[i],cmap=plt.cm.RdYlBu, edgecolor='black', s=15)plt.suptitle("Decision surface of a decision tree using paired features")
plt.legend(loc='lower right', borderpad=0, handletextpad=0)
plt.axis("tight")plt.figure()
clf = DecisionTreeClassifier().fit(iris.data, iris.target)
plot_tree(clf, filled=True)
plt.show()
