单变量线性回归
预测线性方程可以用下式表示：
训练样本的目标值与预测计算所得的目标值之间存在一个误差ε：
ε=hθ(x)-y (服从高斯分布)
为了让误差越来越小，根据最小二乘法得到所需的目标函数：
通过批量梯度下降法使目标函数达到极值点：
通过迭代计算得到我们所需的曲线。
工具：Python3.6+PyCharm+Numpy+Pandas+PyQt5+Matplotlib
代码实现:
#创建所需的线性包 linear
#导入数据
import sys
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
def ToData():
path="Data.txt"
data=pd.read_csv(path,header=None,names=['x','y'])
return data
#定义代价函数
def costfun(X,y,Theta):
inner=np.power(((X*Theta.T)-y),2)
return np.sum(inner)/(2*len(X))
#提取数据，具体可参考Pandas用法
def data_taking(data):
data.insert(0,'Ones',1)
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.matrix(np.zeros(X.shape[1]))
return X,y,Theta
#定义梯度下降函数
def gradientDescent(X,y,Theta,alpha,iters):
temp=np.matrix(np.zeros(Theta.shape))
parameters=int(Theta.ravel().shape[1])
cost=np.zeros(iters)
for iin range(iters):
error=(X*Theta.T)-y
for jin range(parameters):
term=np.multiply(error,X[:,j])
temp[0,j]=Theta[0,j]-((alpha/len(X))*np.sum(term))
Theta=temp
cost[i]=costfun(X,y,Theta)
return Theta,cost
#绘制曲线图
def Draw_close_line():
alpha=0.01
N=1000#迭代次数
data=ToData()
X,y,Theta=data_taking(data)
g,cost=gradientDescent(X,y,Theta,alpha,N)
x=np.linspace(data.x.min(),data.x.max(),100)
f=g[0,0]+(g[0,1]*x)
fig,ax=plt.subplots(figsize=(12,8))
ax.plot(x,f,'r',label='拟合曲线')
ax.scatter(data.x,data.y,label='散点图')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('单变量线性回归')
通过PyQt5绘制曲线：
#导入线性库，及必须的包
import sys
from PyQt5.QtGui import*
from PyQt5.QtWidgets import*
from PyQt5.QtCore import*
import matplotlib
matplotlib.use("Qt5Agg")
from PyQt5 importQtCore
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.backends.backend_qt5agg import NavigationToolbar2QT as NavigationToolbar
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import linear
#创建绘图类MyMplCanvas
class MyMplCanvas(FigureCanvas):
def __init__(self,parent=None, width=5, height=4, dpi=100):
# 配置中文显示
plt.rcParams['font.family'] = ['SimHei'] # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False # 用来正常显示负号
self.fig = plt.figure(figsize=(width,height),dpi=dpi)
#创建两个绘图显示块
self.axes = self.fig.add_subplot(111)
self.axes1= self.fig.add_subplot(111)
FigureCanvas.__init__(self, self.fig)
self.setParent(parent)
FigureCanvas.setSizePolicy(self,
QSizePolicy.Expanding,
QSizePolicy.Expanding)
FigureCanvas.updateGeometry(self)
def Drawing_node(self):#绘制散点图
data=linear.ToData()
x=data.x.values
y=data.y.values
self.axes.set_xticklabels(np.linspace(min(x),max(x),5))
self.axes.set_yticklabels(np.linspace(min(y),max(y),5))
self.axes.scatter(x,y)#散点图
self.axes.set_xlabel('x轴')
self.axes.set_ylabel('y轴')
self.axes.grid(False)#不显示网格
def Drawing_close(self):#绘制拟合图
alpha=0.001
N=200#迭代次数
data=linear.ToData()
X,y,theta=linear.data_taking(data)
g,cost=linear.gradientDescent(X,y,theta,alpha,N)
x=np.linspace(data.x.min(),data.x.max(),100)
f=g[0,0]+(g[0,1]*x)
self.axes1.plot(x,f,'r',label='拟合曲线')
self.axes1.set_xlabel('X')
self.axes1.set_ylabel('y')
self.axes1.set_title('单变量线性回归')
self.axes1.grid(False)
self.axes2=self.axes1.twinx()
self.axes2.scatter(data.x,data.y,label='散点图')
class MainWindow(QWidget):#主窗口
def __init__(self,parent=None):
super(MainWindow,self).__init__(parent)
self.resize(1200,600)
self.setWindowTitle("线性回归")
#定义全局布局
H_layout=QHBoxLayout()
#定义两个局部布局
V1_layout=QVBoxLayout()
V2_layout=QVBoxLayout()
#定义两个布局控件
V1_W=QWidget()
V2_W=QWidget()
#V1_layout布局
self.Button1=QPushButton('读取数据',self)
self.Button1.clicked.connect(self.ReadData)#
V1_layout.addWidget(self.Button1)
self.textEdit=QTextEdit()
V1_layout.addWidget(self.textEdit)
self.Button2=QPushButton('显示散点图',self)
V1_layout.addWidget(self.Button2)
self.Button2.clicked.connect(self.On_node)
self.mpl_1= MyMplCanvas(self, width=4, height=5, dpi=100)
self.mpl_1.Drawing_node()
V1_layout.addWidget(self.mpl_1)
self.mpl_1.setVisible(False)
V1_layout.addStretch(0.5)
V1_W.setLayout(V1_layout)
H_layout.addWidget(V1_W)
#V2_layout布局
self.Button3=QPushButton('绘制拟合曲线',self)
self.Button3.move(800,50)
self.Button3.clicked.connect(self.On_close)
self.mpl_2= MyMplCanvas(self, width=4, height=4, dpi=100)
self.mpl_2.Drawing_close()
self.mpl_2.setVisible(False)
V2_layout.addWidget(self.mpl_2)
V2_W.setLayout(V2_layout)
H_layout.addWidget(V2_W,Qt.AlignRight,Qt.AlignBottom)
H_layout.addStretch(0.5)
self.setLayout(H_layout)
#定义所关联的函数
def ReadData(self):
filename=QFileDialog()
filename.setFileMode(QFileDialog.AnyFile)
filename.setFilter(QDir.Files)
if filename.exec_():
filenames=filename.selectedFiles()
f=open(filenames[0],'r')#打开文件
with f:
data=f.read()#读取数据
self.textEdit.setPlainText(data)#显示数据
return data
def On_node(self):#显示散点图函数
self.mpl_1.setVisible(True)
def On_close(self):#显示拟合曲线函数
self.mpl_2.setVisible(True)
if __name__=='__main__':
app=QApplication(sys.argv)
form=MainWindow()
form.show()
sys.exit(app.exec_())
原代码：https://github.com/jz20170904/PyQT5-and-Linear_regression