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Ovr And Ovo

May 4, 2019

逻辑回归解决多分类问题

二分类算法解决多分类问题的方案：

  • OvR (One vs Rest)

形成 n 个二分类问题

OvR

  • OvO (One vs One)

形成$C_n^2$个二分类问题，选择获胜次数最高的那个分类，准确率更高

OvR

OvR 和 OvO

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

iris = datasets.load_iris()

X = iris.data[:,:2]
y = iris.target

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)

from sklearn.linear_model import LogisticRegression

log_reg = LogisticRegression()
log_reg.fit(X_train, y_train)

LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True, intercept_scaling=1, max_iter=100, multi_class=’ovr’, n_jobs=1, penalty=’l2’, random_state=None, solver=’liblinear’, tol=0.0001, verbose=0, warm_start=False)

log_reg.score(X_test, y_test)

0.6578947368421053

from matplotlib.colors import ListedColormap

def plot_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100 )).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100 )).reshape(-1, 1)
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    custom_camp = ListedColormap(['#EF9A9A', '#FFF59F', '#90CAF9'])
    plt.contourf(x0, x1, zz, cmap=custom_camp)

plot_decision_boundary(log_reg, axis=[4, 8.5, 1.5, 4.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.scatter(X[y==2,0], X[y==2,1])
plt.show()

png

log_reg2 = LogisticRegression(multi_class='multinomial', solver='newton-cg')
log_reg2.fit(X_train, y_train)

LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True, intercept_scaling=1, max_iter=100, multi_class=’multinomial’, n_jobs=1, penalty=’l2’, random_state=None, solver=’newton-cg’, tol=0.0001, verbose=0, warm_start=False)

log_reg2.score(X_test, y_test)

0.7894736842105263

plot_decision_boundary(log_reg2, axis=[4, 8.5, 1.5, 4.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.scatter(X[y==2,0], X[y==2,1])
plt.show()

png

使用所有数据

X = iris.data
y = iris.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)

log_reg = LogisticRegression()
log_reg.fit(X_train, y_train)
log_reg.score(X_test, y_test)

0.9473684210526315

log_reg2 = LogisticRegression(multi_class='multinomial', solver='newton-cg')
log_reg2.fit(X_train, y_train)
log_reg2.score(X_test, y_test)

1.0

scikit-learn 中的 OvR 和 OvO 类

from sklearn.multiclass import OneVsRestClassifier

ovr = OneVsRestClassifier(log_reg)
ovr.fit(X_train, y_train)
ovr.score(X_test, y_test)

0.9473684210526315

from sklearn.multiclass import OneVsOneClassifier

ovo = OneVsOneClassifier(log_reg)
ovo.fit(X_train, y_train)
ovo.score(X_test, y_test)

1.0