10.多项式回归和多分类策略

约 534 字大约 2 分钟

2025-09-20

我们有两种方法来处理多分类问题： OvO和OvR:

方法	时间复杂度	准确率
OvO	$C_n^2T=\frac{n(n-1)}{2}$	更准确
OvR	$nT$	存在类别混淆

import numpy as np
from matplotlib import pyplot as plt

np.random.randn()=np.random.normal(0,1)

np.random.seed(0)
X = np.random.normal(0,1,size=(100,2))
y=np.array((X[:,0]**2+X[:,1]**2<2),dtype=int) # 构造线性不可分数据
y

 array([0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0])

from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

plt.scatter(x_train[:,0],x_train[:,1],c=y_train)
plt.show()

我们发现无法找到一条直线来拟合了.

多项式逻辑回归

from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)
poly.fit(x_train)

 PolynomialFeatures()

x2 = poly.fit_transform(x_train)
x2_t = poly.fit_transform(x_test)

from sklearn.linear_model import LogisticRegression
clf = LogisticRegression()
clf.fit(x2,y_train)
clf.score(x2,y_train)

 0.9875

clf.score(x2_t,y_test)

 0.95

多分类OVR和OVO代码实现

from sklearn.datasets import load_iris
iris = load_iris()
X = iris.data
y = iris.target
X.shape, y.shape

 ((150, 4), (150,))

x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

plt.scatter(x_train[:,0],x_train[:,1],c=y_train)
plt.show()

# OVR
from sklearn.multiclass import OneVsRestClassifier
ovr = OneVsRestClassifier(LogisticRegression())
ovr.fit(x_train,y_train)
ovr.score(x_test,y_test)

 0.9666666666666667

# OVO
from sklearn.multiclass import OneVsOneClassifier
ovo = OneVsOneClassifier(LogisticRegression())
ovo.fit(x_train,y_train)
ovo.score(x_test,y_test)

1.0