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
