吴恩达老师机器学习-ex1

线性回归

有借鉴网上部分博客

第一题 单变量

先导入相关库

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

读取数据，并展示前五行

data=pd.read_csv(path,header=None,names=["Population","Profit"])
data.head()

先绘制一个散点图，查看数据分布，并规定x，y轴的名字

data.plot(kind="scatter",x="Population",y="Profit",figsize=(12,8))
plt.show

新增一列，已便构造矩阵

#新增一列x0
data.insert(0,"x0",1)
data.head()

先查看数据有多少列，然后读取相应的列的数据构造矩阵，同时构造一个零矩阵

cols=data.shape[1]
X=data.iloc[:,0:cols-1]
Y=data.iloc[:,cols-1:cols]
 
X=np.matrix(X.values)
Y=np.matrix(Y.values)
theta=np.zeros((2, 1))

构造代价函数。 代价函数公式：

def cost_fuc(X,Y,theta):
    cost_matrix=np.power(X*theta-Y,2)
    cost_finite=np.sum(cost_matrix)/(2*len(X))
    return cost_finite

构造梯度下降函数

def gradient_descent(X,Y,theta,alpha,times):
    for i in range(times):
        theta[0]=theta[0]-alpha*(1/len(X))*(np.sum(X*theta-Y))
        theta[1]=theta[1]-alpha*(1/len(X))*(np.multiply((X*theta-Y),X[1])).sum()
        temp0=theta[0]
        temp1=theta[1]
        cost = cost_func(X, Y, theta)
        pass
    return theta

调用函数，并绘制线性回归图

theta_last= gradient_descent(x,y,theta,0.02,1500)
 
data.plot(kind="scatter",x="Population",y="Profit",figsize=(12,8),label='Prediction')
x = np.linspace(data.Population.min(), data.Population.max(), 100)
y = theta[0] + theta[1] * x
 
plt.plot(x, y)
plt.show()

第二题 多变量

导入相关库并读取文件数据

​
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
path = "./ex1data2.txt"
data = pd.read_csv(path,header=None,names=["size","bedrooms","price"])
data.head()
#展示两个散点图
path = "./ex1data2.txt"
data = pd.read_csv(path,header=None,names=["size","bedrooms","price"])
data.head()
data.plot(kind="scatter",x="bedrooms",y="price")
plt.show()

由于特征值的数字大小差距较大，进行特征缩放，并构造相关的xy数组

#特征缩放
data = (data - data.mean())/data.std()
data.head()
data.insert(0,"x0",1)
data.head()
cols=data.shape[1]
X=data.iloc[:,0:cols-1]
Y=data.iloc[:,cols-1:cols]
 
X=X.values
Y=Y.values
theta=np.zeros((3, 1))

代价函数

#代价函数
def cost_func(x,y,theta):
    cost_matrix = np.power(x@theta-y,2)
    cost_finite = np.sum(cost_matrix)/(2*len(x))
    return cost_finite

梯度下降函数

#梯度下降
def gradient_descent(X,Y,theta,alpha,times):
    costs = []
    for i in range(times):
        theta = theta - (X.T @ (X@theta - Y)) * alpha / len(X)  #迭代梯度下降
        cost = cost_func(X, Y, theta)
        costs.append(cost)
        pass
    return theta,costs
 

显示图像

alpha_iters = [0.003,0.03,0.0001,0.001,0.01]#设置alpha
counts = 200#循环次数
fig,ax = plt.subplots()
for alpha in alpha_iters:#迭代不同学习率alpha
    _,costs = gradient_descent(X,Y,theta,alpha,counts)#得到损失值
    ax.plot(np.arange(counts),costs,label = alpha)#设置x轴参数为迭代次数，y轴参数为cost
    ax.legend()  #加上这句  显示label
    
ax.set(xlabel= 'counts',   #图的坐标轴设置
       ylabel = 'cost',
       title = 'cost vs counts')#标题
plt.show()#显示图像