逻辑回归+牛顿法 python实现

#!/usr/bin/python
# -*- coding: utf-8 -*-

# matplotlib.pyplot 用于绘制2D图表
import matplotlib.pyplot as plt
from numpy import *

class LR:
# 数据的行数
__row = 0
# 数据的列数
__col = 0
# 迭代次数
__numIterations = 10
# 训练集合
__trainData = []
# θ参数
__theta = []
# Y值
__Y = []
# 损失
__Cost = []

def __init__(self, data):
self.__row, self.__col = shape(data)
self.__trainData = data[:, 0:self.__col - 1]
self.__Y = data[:, self.__col - 1:self.__col]
self.__col = self.__col - 1
# 系数的初始值为0  如果是其他值有可能会算不出结果
self.__theta = mat(zeros((self.__col, 1)))

# 设置迭代次数
def setnumIterations(self, numIterations):
self.__numIterations = numIterations

# 获取theta
def getTheta(self):
return self.__theta

# 获取cost损失
def getCost(self):
return self.__Cost

# 训练数据模型
def train(self):
# 存储损失
self.__Cost = mat(zeros((self.__numIterations, 1)))
for i in range(0, self.__numIterations):
# 更新Theta
self.__updateTheta(i)

# 迭代theta
def __updateTheta(self, i):
# 获取预测值h(x) 1.0 / (1 + exp(-z))
h = 1.0 / (1 + exp(-(self.__trainData * self.__theta)))
# 获取损失
self.__getCost(i, h)
# .T 矩阵的转置
# 一阶导数矩阵算法 (1 / m) * x.T * (h-y)
J = multiply(1.0 / self.__row,
self.__trainData.T * (h - self.__Y))
# 获取Hession矩阵
# getA() 矩阵转换为数组
# diag(x) 生成对角线为x其余为0的矩阵
# Hession矩阵算法(1 / m) * x.T * U * x   U表示用(h * (1 - h))构成对角，其余为0的矩阵
H = multiply(1.0 / self.__row, self.__trainData.T *
diag(multiply(h, (1 - h)).T.getA()
[0]) * self.__trainData)
# .I 矩阵的逆
self.__theta = self.__theta - H.I * J

# 计算损失
def __getCost(self, i, h):
l1 = self.__Y.T * log(h)
l2 = (1 - self.__Y).T * log((1 - h))
self.__Cost[i, :] = multiply(1.0 / self.__row, sum(-l1 - l2))

# 画图
def draw(self):
x1 = []
y1 = []
x2 = []
y2 = []
for i in range(0, self.__row):
if(self.__Y[i] == 1):
x1.append(self.__trainData[i, 1])
y1.append(self.__trainData[i, 2])
else:
x2.append(self.__trainData[i, 1])
y2.append(self.__trainData[i, 2])
# plt.figure()创建一个绘图对象
# 第一个参数表示绘图对象的序号，当序号相同时候不会创建新的对象，而是指向该序号的对象。
# 第二个参数表示绘图对象的尺寸。参数值 * 80
plt.figure(0, figsize=(8, 5))
fig = plt.figure(0)
# 创建一个画布,参数含义(m,n,k）将画布分为m * n块，这个图像在第k块
ax = fig.add_subplot(1, 1, 1)
# scatter散列图 s 数据点的大小 c颜色 marker形状
ax.scatter(x1, y1, s=30, c="red", marker="o")
ax.scatter(x2, y2, s=30, c="green")
x = arange(20, 80, 10)
a = float(self.__theta[1])
b = float(self.__theta[0])
c = float(self.__theta[2
4000
])
y = (a * x + b) / (-c)
# plt.plot(x,y,label="$sin(x)$",color="red",linewidth=2)
# label : 曲线名字 添加"$"符号，matplotlib就会使用其内嵌的latex引擎绘制的数学公式
# color : 指定曲线的颜色        linewidth : 指定曲线的宽度
# plt.plot(x,z,"b--",label="$cos(x^2)$") 第三个参数"b--"指定曲线的颜色和线型(蓝色 虚线)
ax.plot(x, y)
plt.xlabel("X")
plt.ylabel("Y")
plt.legend(["hx", "x1y1", "x2y2"])
plt.show()

# -------------------------开始-----------------------
x = open("/home/hadoop/Python/LR/ex4x.dat", "r")
y = open("/home/hadoop/Python/LR/ex4y.dat", "r")
data = []
for i in x:
temp = [1]
val = i.split()
for j in val:
temp.append(float(j))
temp.append(float(y.readline()))
data.append(temp)

lr = LR(mat(data))
lr.setnumIterations(7)
lr.train()
print(lr.getTheta())
print(lr.getCost())
lr.draw()