-
"""逻辑回归中的Sigmoid函数"""
-
import numpy as np
-
import matplotlib.pyplot as plt
-
def sigmoid(t):
-
return 1/(1+np.exp(-t))
-
x=np.linspace(-10,10,500)
-
y=sigmoid(x)
-
plt.plot(x,y)
-
plt.show()
结果：
逻辑回归损失函数的梯度：
逻辑回归算法：
-
import numpy as np
-
from metrics import accuracy_score
-
class LogisticRegression:
-
def __init__(self):
-
"""初始化Logistic Regression模型"""
-
self.coef_ = None
-
self.intercept_ = None
-
self._theta = None
-
def _sigmoid(self,t):
-
return 1. / (1. + np.exp(-t))
-
def fit(self, X_train, y_train, eta=0.01, n_iters=1e4):
-
"""根据训练数据集X_train, y_train, 使用梯度下降法训练Linear Regression模型"""
-
assert X_train.shape[0] == y_train.shape[0], \
-
"the size of X_train must be equal to the size of y_train"
-
def J(theta, X_b, y):
-
"""求损失函数"""
-
y_hat=self._sigmoid(X_b.dot(theta))
-
try:
-
return -np.sum(y*np.log(y_hat) + (1-y)*np.log(1-y_hat))/ len(y)
-
except:
-
return float(‘inf‘)
-
def dJ(theta, X_b, y):
-
"""求梯度"""
-
# res = np.empty(len(theta))
-
# res[0] = np.sum(X_b.dot(theta) - y)
-
# for i in range(1, len(theta)):
-
# res[i] = (X_b.dot(theta) - y).dot(X_b[:, i])
-
# return res * 2 / len(X_b)
-
return X_b.T.dot(self._sigmoid(X_b.dot(theta)) - y) / len(X_b)
-
def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):
-
"""使用批量梯度下降法寻找theta"""
-
theta = initial_theta
-
cur_iter = 0
-
while cur_iter < n_iters:
-
gradient = dJ(theta, X_b, y)
-
last_theta = theta
-
theta = theta - eta * gradient
-
if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
-
break
-
cur_iter += 1
-
return theta
-
X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
-
initial_theta = np.zeros(X_b.shape[1])
-
self._theta = gradient_descent(X_b, y_train, initial_theta, eta, n_iters)
-
self.intercept_ = self._theta[0]
-
self.coef_ = self._theta[1:]
-
return self
-
def predict_proba(self, X_predict):
-
"""给定待预测数据集X_predict，返回表示X_predict的结果概率向量"""
-
assert self.intercept_ is not None and self.coef_ is not None, \
-
"must fit before predict!"
-
assert X_predict.shape[1] == len(self.coef_), \
-
"the feature number of X_predict must be equal to X_train"
-
X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
-
return self._sigmoid(X_b.dot(self._theta))
-
def predict(self, X_predict):
-
"""给定待预测数据集X_predict，返回表示X_predict的结果向量"""
-
assert self.intercept_ is not None and self.coef_ is not None, \
-
"must fit before predict!"
-
assert X_predict.shape[1] == len(self.coef_), \
-
"the feature number of X_predict must be equal to X_train"
-
proba=self.predict_proba(X_predict)
-
return np.array(proba>=0.5,dtype=‘int‘)
-
def score(self, X_test, y_test):
-
"""根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""
-
y_predict = self.predict(X_test)
-
return accuracy_score(y_test, y_predict)
-
def __repr__(self):
-
return "LogisticRegression()"
-
"""实现逻辑回归"""
-
import numpy as np
-
import matplotlib.pyplot as plt
-
from sklearn import datasets
-
iris=datasets.load_iris()
-
X=iris.data
-
y=iris.target
-
X=X[y<2,:2]
-
y=y[y<2]
-
plt.scatter(X[y==0,0],X[y==0,1],color=‘red‘)
-
plt.scatter(X[y==1,0],X[y==1,1],color=‘blue‘)
-
plt.show()
-
"""使用逻辑回归"""
-
from model_selection import train_test_split
-
from LogisticRegression import LogisticRegression
-
X_train,X_test,y_train,y_test=train_test_split(X,y,seed=666)
-
log_reg=LogisticRegression()
-
log_reg.fit(X_train,y_train)
-
print(log_reg.score(X_test,y_test))
-
print(log_reg.predict_proba(X_test))
结果：
-
E:\pythonspace\KNN_function\venv\Scripts\python.exe E:/pythonspace/KNN_function/try.py
-
1.0
-
[0.92972035 0.98664939 0.14852024 0.17601199 0.0369836 0.0186637
-
0.04936918 0.99669244 0.97993941 0.74524655 0.04473194 0.00339285
-
0.26131273 0.0369836 0.84192923 0.79892262 0.82890209 0.32358166
-
0.06535323 0.20735334]
-
Process finished with exit code 0
逻辑回归中的决策边界和添加多项式特征：
-
"""在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=(100,2))
-
y=np.array(X[:,0]**2+X[:,1]**2<1.5,dtype=‘int‘)
-
"""使用逻辑回归"""
-
from LogisticRegression import LogisticRegression
-
log_reg=LogisticRegression()
-
log_reg.fit(X,y)
-
"""绘制思路"""
-
def plot_decision_boundary(model,axis):
-
x0,x1 = np.meshgrid(
-
np.linspace(axis[0],axis[1],int((axis[1]-axis[0])*100)),
-
np.linspace(axis[2],axis[3],int((axis[3]-axis[2])*100))
-
)
-
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()
-
"""添加特征值，即升维"""
-
from sklearn.preprocessing import PolynomialFeatures
-
from sklearn.preprocessing import StandardScaler
-
from sklearn.pipeline import Pipeline
-
def PolynomialLogisticRegression(degree):
-
return Pipeline([
-
(‘Poly‘,PolynomialFeatures(degree=degree)),
-
(‘std_scaler‘,StandardScaler()),
-
(‘Logistic‘,LogisticRegression())
-
])
-
poly_log_reg = PolynomialLogisticRegression(degree=2)
-
poly_log_reg.fit(X,y)
-
plot_decision_boundary(poly_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()
结果：
-
"""逻辑回归中使用正则化"""
-
import numpy as np
-
import matplotlib.pyplot as plt
-
from sklearn.model_selection import train_test_split
-
from sklearn.linear_model import LogisticRegression
-
from sklearn.preprocessing import StandardScaler
-
from sklearn.pipeline import Pipeline
-
from sklearn.preprocessing import PolynomialFeatures
-
np.random.seed(666)
-
X=np.random.normal(0,1,size=(200,2))
-
y=np.array(X[:,0]**2+X[:,1]<1.5,dtype=‘int‘)
-
for _ in range(20):
-
y[np.random.randint(200)] = 1
-
plt .scatter(X[y==0,0],X[y==0,1])
-
plt .scatter(X[y==1,0],X[y==1,1])
-
plt.show()
-
X_train,X_test,y_train,y_test=train_test_split(X,y)
-
log_reg=LogisticRegression()
-
log_reg.fit(X,y)
-
def plot_decision_boundary(model,axis):
-
x0,x1 = np.meshgrid(
-
np.linspace(axis[0],axis[1],int((axis[1]-axis[0])*100)),
-
np.linspace(axis[2],axis[3],int((axis[3]-axis[2])*100))
-
)
-
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)
-
def PolynomialLogisticRegression(degree,C=1.0,penalty=‘l2‘):
-
return Pipeline([
-
(‘Poly‘,PolynomialFeatures(degree=degree)),
-
(‘std_scaler‘,StandardScaler()),
-
(‘Logistic‘,LogisticRegression(C=C,penalty=penalty))
-
])
-
poly_log_reg = PolynomialLogisticRegression(degree=20,C=0.1,penalty=‘l1‘)
-
poly_log_reg.fit(X_train,y_train)
-
plot_decision_boundary(poly_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()
结果
应用OVR和OVO使逻辑回归处理多分类问题
-
"""OVR和OVO"""
-
#为了数据可视化方便，我们只使用鸢尾花数据集的前两列特征
-
from sklearn import datasets
-
from sklearn.linear_model import LogisticRegression
-
from sklearn.model_selection import train_test_split
-
import matplotlib.pyplot as plt
-
import numpy as np
-
iris = datasets.load_iris()
-
X = iris[‘data‘][:,:2]
-
y = iris[‘target‘]
-
X_train,X_test,y_train,y_test=train_test_split(X,y,random_state=666)
-
#log_reg = LogisticRegression(multi_class=‘ovr‘) #传入multi_class参数可以指定使用ovr或ovo，默认ovr #由于只使用前两列特征，导致分类准确度较低
-
log_reg = LogisticRegression(multi_class=‘ovr‘,solver=‘newton-cg‘)
-
log_reg.fit(X_train,y_train)
-
log_reg.score(X_test,y_test)
-
def plot_decision_boundary(model,axis):
-
x0,x1 = np.meshgrid(
-
np.linspace(axis[0],axis[1],int((axis[1]-axis[0])*100)),
-
np.linspace(axis[2],axis[3],int((axis[3]-axis[2])*100))
-
)
-
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=[4,8.5,1.5,4.5])
-
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()
-
"""使用全部数据 OVR and OVO"""
-
from sklearn.multiclass import OneVsOneClassifier
-
from sklearn.multiclass import OneVsRestClassifier
-
from sklearn import datasets
-
from sklearn.linear_model import LogisticRegression
-
from sklearn.model_selection import train_test_split
-
iris = datasets.load_iris()
-
X = iris.data
-
y = iris.target
-
X_train,X_test,y_train,y_test=train_test_split(X,y,random_state=666)
-
ovr = OneVsRestClassifier(log_reg) #参数为二分类器
-
ovr.fit(X_train,y_train)
-
print(ovr.score(X_test,y_test))
-
ovo = OneVsOneClassifier(log_reg)
-
ovo.fit(X_train,y_train)
-
print(ovo.score(X_test,y_test))
结果：
-
E:\pythonspace\KNN_function\venv\Scripts\python.exe E:/pythonspace/KNN_function/try.py
-
E:\pythonspace\KNN_function\venv\lib\site-packages\matplotlib\contour.py:960: UserWarning: The following kwargs were not used by contour: ‘linewidth‘
-
s)
-
0.9736842105263158
-
1.0
-
Process finished with exit code 0
原文地址：https://www.cnblogs.com/kekexuanxaun/p/9459365.html