LogisticRegression Algorithm——机器学习（西瓜书）读书笔记

import numpy as np
from sklearn.datasets import load_breast_cancer
import sklearn.linear_model
from numpy.linalg import  inv
# numpy.linalg 是处理线性代数的包，inv为矩阵求逆

#sigmoid函数
def sigmoid(x):
    # Sigmoid function
    return 1.0/(1 + np.exp(-x))

# 梯度函数
def gradient(t, y, phi):
    grad = phi.T * (y - t)
    return grad 

# 计算海森矩阵
def Hessian(t, y, phi):
    H = phi.T * (np.diag(np.diag(y * (1 - y).T))) * phi
    return H

def Newton_Raphson(t, w, phi):
    #Newton_Raphson algorithm   牛顿法迭代
    for i in range(0,100):
        y = sigmoid(phi * w)
        grad = gradient(t, y, phi)
        H = Hessian(t, y, phi)
        w = w - inv(H+0.0001*np.eye(H.shape[0])) * grad
    return w

# 测试算法（一个例子：sklearn中预测癌症数据包）

# 导入数据
cancer = load_breast_cancer()

# 查看关键字
print (cancer.keys())

#标准化处理数据
phi = np.mat(cancer.data)
t = np.mat(cancer.target)
phi = (phi - np.mean(phi, axis = 0))/(np.std(phi, axis = 0))

# 切分数据集为训练集与测试集
phi_train = np.mat(phi[0:200])
t_train =np.mat(cancer.target[0:200].reshape((len(phi_train),1)))
phi_test = np.mat(phi[200:-1])
t_test = np.mat(cancer.target[200:-1].reshape((len(phi_test),1)))

# 添加偏置项
b1 = np.ones(len(phi_train))
b2 = np.ones(len(phi_test))
phi_train_b = np.c_[phi_train, b1]
phi_test_b = np.c_[phi_test, b2]

# 初始化权重
np.random.seed(666)     #使随机数产生后就固定下来
w = np.mat(np.random.normal(0, 0.01, phi_train_b.shape[-1])).T
W = Newton_Raphson(t_train, w, phi_train_b)

# 计算预测正确的训练样本比例
y_pred = sigmoid(phi_train_b * W)
t_pred = np.where(y_pred > 0.5, 1 ,0)
accuracy_train = np.mean(t_train == t_pred)
print('The accuracy of train set is:',accuracy_train)

# 计算预测正确测试样本比例
y_pred = sigmoid(phi_test_b * W)
t_pred = np.where(y_pred > 0.5, 1 ,0)
accuracy_test = np.mean(t_test == t_pred)
print('The accuracy of test set is:',accuracy_test)

# 计算最后预测的准确率
model = sklearn.linear_model.LogisticRegression(solver='newton-cg')
model.fit(phi_train_b, t_train)
y_pred = model.predict(phi_test_b)
acc = np.mean(t_test== y_pred.reshape([-1,1]))
print (acc)