逻辑回归中添加多项式特征

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(666)
X = np.random.normal(0,1,size=(200,2))
y = np.array(X[:,0]**2+X[:,1]**2 <1.5,dtype='int')

plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

使用逻辑回归

from sklearn.linear_model import LogisticRegression

log_reg = LogisticRegression()
log_reg.fit(X,y)

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,y)

0.605

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) 
    from matplotlib.colors import ListedColormap 
    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9']) 
    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)

plot_decision_boundary(log_reg,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
  s)

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler
def PolynomialLogisticRegression(degree):
    return Pipeline([
        ('poly',PolynomialFeatures(degree)),
        ('std_scaler',StandardScaler()),
        ('log_reg',LogisticRegression())
    ])

ploy_log_reg = PolynomialLogisticRegression(degree=2)
ploy_log_reg.fit(X,y)

Pipeline(memory=None,
     steps=[('poly', PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', 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))])

ploy_log_reg.score(X,y)

0.95

plot_decision_boundary(ploy_log_reg,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
  s)

ploy_log_reg2 = PolynomialLogisticRegression(degree=20)
ploy_log_reg2.fit(X,y)

Pipeline(memory=None,
     steps=[('poly', PolynomialFeatures(degree=20, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', 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))])

plot_decision_boundary(ploy_log_reg2,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
  s)