实现逻辑回归算法
实现代码
在python chame中创建LogisticRegression.py文件，写入想要实现的功能
其中，可以将原先的LinearRegression复制过来，详情可见以前的关于线性回归的博客，修改类名，不用的功能直接删除，添加上sigmoid函数以及计算结果概率向量的函数，对损失函数的计算，梯度的计算，预测结果进行修改，使用这里的计算思想即可
代码如下：
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.interception_ = 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):
"""根据训练数据集使用梯度算法训练模型"""
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):
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):
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):
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.interception_ = self._theta[0]
self.coef_ = self._theta[1:]
return self
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.interception_ 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 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.interception_ 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 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()"
from matplotlib.colors import ListedColormap
def plot_decision_boundary(model, axis):
x0 = np.meshgrid(np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape())
x1 = np.meshgrid(np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape())
X_new = np.c_[x0.ravel(), x1.ravel()]
y_predict = model.predict(X_new)
zz = y_predict.reshape(x0.shape)
custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])
plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)
具体使用
（在notebook中）
加载上相应的包，使用鸢尾花数据集，由于其有三种分类，因此只选用y<2的行，且只取前两个特征，并绘制图像
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')
图像如下
分割好数据集以后（使用种子666），调用封装好的方法，进行实例化以后对训练数据集进行fit操作
from model_selection import train_test_split
X_train,X_test,y_train,y_test = train_test_split(X,y,seed=666)
from LogisticRegression import LogisticRegression
log_reg = LogisticRegression()
log_reg.fit(X_train,y_train)
使用代码计算分类结果
log_reg.score(X_test,y_test)
结果如下
分类结果中的数据
log_reg.predict_proba(X_test)
结果如下
其中y_test中为
然后使用概率矩阵以后的真正得到的log_reg.predict(X_test)中的结果如下
以上为实现的逻辑回归算法的简单的应用
