[人工智能]吴恩达机器学习课后编程作业(Week2)

#!/usr/bin/env python 3.74
# -*-coding:utf-8 -*-
#@Time: 2021/09/26 13:05:35 
#@Author: zz 
#@File : .py
#@Software : VScode

#Week2 
#1.逻辑回归
#建立一个逻辑回归模型来预测一个学生是否被大学录取。
#根据两次考试的结果来决定每个申请人的录取机会。有以前的申请人的历史数据， 可以用它作为逻辑回归的训练集
#python实现逻辑回归 目标：建立分类器（求解出三个参数 θ0 θ1 θ2）即得出分界线 备注:θ1对应'Exam 1'成绩,θ2对应'Exam 2' 设定阈值，根据阈值判断录取结果 备注:阈值指的是最终得到的概率值.将概率值转化成一个类别.一般是＞0.5是被录取了,＜0.5未被录取

import pandas as pd
import numpy as np 
import matplotlib.pyplot as plt 
import seaborn as sns  #Seaborn其实是在matplotlib的基础上进行了更高级的API封装，从而使得作图更加容易，在大多数情况下使用seaborn就能做出很具有吸引力的图。
plt.style.use("fivethirtyeight")   #样式美化
from sklearn.metrics import classification_report  #这个包是评价报告

#准备数据
#data = pd.read_csv('learn_myself\week2\ex2data1.txt', names=['exam1', 'exam2', 'admitted'])
data = pd.read_csv('ex2data1.txt', names=['exam1', 'exam2', 'admitted'])
data.head()  #看前五行
data.describe()

sns.set(context="notebook", style="darkgrid", palette=sns.color_palette("RdBu", 2)) #设置样式参数,默认主题 darkgrid（灰色背景+白网格）,调色板 2色
sns.lmplot('exam1', 'exam2', hue='admitted', data=data,    #hue就是显示出来的点 0还是1
           size=6, 
           fit_reg=False,    #fit_feg 参数，控制是否显示拟合的直线
           scatter_kws={"s": 50}    #hue参数是将name所指定的不同类型的数据叠加在一张图中显示
          )
plt.show()#看下数据的样子


def get_X(df): #读取特征
   ones = pd.DataFrame({'ones': np.ones(len(df))})  #ones是m行1列的dataframe   len（df)就是样本的个数 
   #DataFrame是Python中Pandas库中的一种数据结构，它类似excel，是一种二维表
   data = pd.concat([ones, df], axis=1)   # 合并数据，根据列合并 axis = 1的时候，concat就是行对齐，然后将不同列名称的两张表合并 加列
   data.insert(0, 'Ones', 1)
   return data.iloc[:, :-1].values# 这个操作返回 ndarray,不是矩阵   NDFrame.as_matrix Use NDFrame.values instead 

def get_y(df): #读取标签

   return np.array(df.iloc[:, -1])  #df.iloc[:, -1]是指df的最后一列

def normalize_feature(df):
   return df.apply(lambda column: (column - column.mean()) / column.std())  #特征缩放在逻辑回归同样适用


X = get_X(data)
print(X.shape)

y = get_y(data)
print(y.shape)


#sigmoid函数
def sigmoid(z):
   
   return 1 / (1 + np.exp(-z))

#画图
fig,ax = plt.subplots(figsize=(8,6))
ax.plot(np.arange(-10,10,step = 0.01),sigmoid(np.arange(-10,10,step=0.01))) 
#画图 前面为x轴内容，后面为y轴内容  
#np.arange()函数返回一个有终点和起点的固定步长的排列

ax.set_ylim((-0.1,1.1)) #lim 轴线显示长度
ax.set_xlabel('z',fontsize=18)
ax.set_ylabel('g(z)',fontsize=18)
ax.set_title('sigmoid function0',fontsize = 18)
plt.show()

#cost function(代价函数)

theta = theta = np.zeros(4)   
theta 

def cost(theta,X,y):
   
   return np.mean(-y * np.log(sigmoid(X @ theta)) - (1-y) * np.log(1-sigmoid(X @ theta)))
#mean()函数功能：求取均值
cost(theta,X,y)  #这里的输出是0.6931471805599453


#梯度下降 转化为向量化计算

def gradient(theta,X,y):
   return (1/len(X)) * X.T @ (sigmoid(X @ theta) - y)

gradient(theta,X,y)

#拟合参数
import scipy.optimize as opt
res = opt.minimize(fun=cost, x0=theta, args=(X, y), method='Newton-CG', jac=gradient)
print(res)

#用训练集预测和验证
def predict(x,theta):
   prob = sigmoid(x @ theta)
   return (prob >= 0.5).astype(int)  #astype 布尔类型   如果大于0.5 y就等于1

final_theta = res.x
y_pred = predict(X, final_theta)

print(classification_report(y, y_pred))


#寻找决策边界  X*theta = 0

print(res.x)  #最后的theta

coef = -(res.x / res.x[2])  # find the equation
print(coef)

x = np.arange(130, step=0.1)
y = coef[0] + coef[1]*x 
data.describe()  # find the range of x and y

sns.set(context="notebook", style="ticks", font_scale=1.5)  #默认使用notebook上下文 主题 context可以设置输出图片的大小尺寸(scale)

sns.lmplot('exam1', 'exam2', hue='admitted', data=data, 
           size=6, 
           fit_reg=False, 
           scatter_kws={"s": 25}
          )

plt.plot(x, y, 'grey')
plt.xlim(0, 130) 
plt.ylim(0, 130)
plt.title('Decision Boundary')
plt.show()    #这边没有画出决策边界  不明白问题出在哪里  因为我是4个点


#3.正则化逻辑回归
df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])
df.head()
sns.set(context="notebook", style="ticks", font_scale=1.5)

sns.lmplot('test1', 'test2', hue='accepted', data=df, 
           size=6, 
           fit_reg=False, 
           scatter_kws={"s": 50}
          )

plt.title('Regularized Logistic Regression')
plt.show()

#进行特征映射
def feature_mapping(x, y, power, as_ndarray=False):
#     """return mapped features as ndarray or dataframe"""

    data = {"f{}{}".format(i - p, p): np.power(x, i - p) * np.power(y, p)
               for i in np.arange(power + 1)
               for p in np.arange(i + 1)
            }

    if as_ndarray:
        return pd.DataFrame(data).iloc[:,:].values   #.as_matrix()  改成.iloc[:,:].values
    else:
        return pd.DataFrame(data)
     
x1 = np.array(df.test1)
x2 = np.array(df.test2)

data = feature_mapping(x1, x2, power=6)
print(data.shape)
data.head()  #将二维特征映射成28维特征


#正则化代价函数   加了正则项
theta = np.zeros(data.shape[1])
X = feature_mapping(x1, x2, power=6, as_ndarray=True)
print(X.shape)

y = get_y(df)
print(y.shape)

def regularized_cost(theta, X, y, l=1):   #这里的L是兰姆达，这里取兰姆达为1
    # your code here  (appro ~ 3 lines
    theta_j1_to_n = theta[1:]  #数组都是从0下标开始的，这里1代表thetay
    regularized_term = (l / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()
    
    return  cost(theta, X, y) + regularized_term
 
regularized_cost(theta, X, y, l=1)


#正则化梯度
def regularized_gradient(theta, X, y, l=1):
    # your code here  (appro ~ 3 lines)
    theta_j1_to_n = theta[1:]      #不加theta0
    regularized_theta = (l / len(X)) * theta_j1_to_n
    
    regularized_term = np.concatenate([np.array([0]), regularized_theta])
    return gradient(theta, X, y) + regularized_term
 
 
regularized_gradient(theta, X, y)

#拟合参数
import scipy.optimize as opt  #SciPy的optimize模块提供了许多数值优化算法

print('init cost = {}'.format(regularized_cost(theta, X, y)))

res = opt.minimize(fun=regularized_cost, x0=theta, args=(X, y), method='Newton-CG', jac=regularized_gradient)
res


#预测
final_theta = res.x
y_pred = predict(X, final_theta)

print(classification_report(y, y_pred))


#画出决策边界
def draw_boundary(power, l):
#     """
#     power: polynomial power for mapped feature
#     l: lambda constant
#     """
    density = 1000
    threshhold = 2 * 10**-3

    final_theta = feature_mapped_logistic_regression(power, l)
    x, y = find_decision_boundary(density, power, final_theta, threshhold)

    df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])
    sns.lmplot('test1', 'test2', hue='accepted', data=df, size=6, fit_reg=False, scatter_kws={"s": 100})

    plt.scatter(x, y, c='R', s=10)
    plt.title('Decision boundary')
    plt.show()
    
    
def feature_mapped_logistic_regression(power, l):
#     """for drawing purpose only.. not a well generealize logistic regression
#     power: int
#         raise x1, x2 to polynomial power
#     l: int
#         lambda constant for regularization term
#     """
    df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])
    x1 = np.array(df.test1)
    x2 = np.array(df.test2)
    y = get_y(df)

    X = feature_mapping(x1, x2, power, as_ndarray=True)
    theta = np.zeros(X.shape[1])

    res = opt.minimize(fun=regularized_cost,
                       x0=theta,
                       args=(X, y, l),
                       method='TNC',
                       jac=regularized_gradient)
    final_theta = res.x

    return final_theta    
 
 
def find_decision_boundary(density, power, theta, threshhold):
    t1 = np.linspace(-1, 1.5, density)  #1000个样本
    t2 = np.linspace(-1, 1.5, density)

    cordinates = [(x, y) for x in t1 for y in t2]
    x_cord, y_cord = zip(*cordinates)
    mapped_cord = feature_mapping(x_cord, y_cord, power)  # this is a dataframe

    inner_product = mapped_cord.iloc[:,:].values @ theta 

    decision = mapped_cord[np.abs(inner_product) < threshhold]

    return decision.f10, decision.f01
#寻找决策边界函数
draw_boundary(power=6, l=1)     #set lambda = 1
draw_boundary(power=6,l=0)  # set lambda < 0.1
draw_boundary(power=6, l=100)  # set lambda > 10